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Material: Editorial SM6 26 6 p Z 3f11?Px0 L$D 07c0 p 0xxL$D 0_c0 ^SISTEMAS DE ECUACIONES(2  p  ` 3f11? x L$D 03c0 p 0P xxp L$D 09c0 T INECUACIONES (2  Z p B$d@޽h @ ? ̙33$ $___PPT10#+0D"' = @B D"' = @BA?%,( < +O%,( < +D!' =%(%(D%' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*p%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*pD' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*pD' =+4 8?RCB?BCB#ppt_xB*Y3>B ppt_x<*pD' =+4 8?RCB?BCB#ppt_yB*Y3>B ppt_y<*pD%' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*p%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*pD' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*pD' =+4 8?RCB?BCB#ppt_xB*Y3>B ppt_x<*pD' =+4 8?RCB?BCB#ppt_yB*Y3>B ppt_y<*pD' =%( D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*p%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*pD' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*pD' =+4 8?RCB?BCB#ppt_xB*Y3>B ppt_x<*pD' =+4 8?RCB?BCB#ppt_yB*Y3>B ppt_y<*pD%' =%( D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*p%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*pD' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*pD' =+4 8?RCB?BCB#ppt_xB*Y3>B ppt_x<*pD' =+4 8?RCB?BCB#ppt_yB*Y3>B ppt_y<*pD' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*p%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*pD' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*pD' =+4 8?RCB?BCB#ppt_xB*Y3>B ppt_x<*pD' =+4 8?RCB?BCB#ppt_yB*Y3>B ppt_y<*pD' =%(|DL' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<* p%(D' =-{6Bstrips(upLeft)*<3<* p++0+p0 ++0+ p0 ++0+p0 ++0+p0 +.0 @:(  x  c $T  .  H(~_ж_ж?`,$D 0  Una ecuacin es una igualdad entre dos expresiones en la que aparecen nmeros y letras ligados por operaciones. Las letras representan cantidades indeterminadas, y se llaman incgnitas. Una igualdad que es cierta para cualquier valor de las variables es una identidad.JZ x^"  C x~_ж_жdo? < ,$D0 23x2  18x + 19 = 12x  294Z( ((   # @ ` ,$D 0N     2  T_ж_ж Ԕ? B   # l_ж_жDA)?     T`(~_ж_ж?  = Incgnita Z     # : GB ,$D 0N      2   T_ж_ж Ԕ? B  # l_ж_жDA)?    T-~_ж_ж?  <Igualdad Z   X  # ` 1 P,$D 0r  T_ж_жz Ԕ? 0   T\2~_ж_жz ?  X  Y 1er miembro2 Z      #  g,$D 0r  T_ж_жz Ԕ? '   T8~_ж_жz ?D   X 2o miembro2 Z ( H  0@޽h ? ^WNff3___PPT10+!DA' A~= @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-s6Bwipe(left)*<3<*D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-s6Bwipe(left)*<3<*D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-s6Bwipe(left)*<3<*DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =%(DH' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*D#' =+4 8?nCB!#ppt_y+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*D' =+4 8?\CB#ppt_wBCB#ppt_wB*Y3>B ppt_w<*D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*Dp' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<* D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<* D' =+4 8?RCB?BCB#ppt_xB*Y3>B ppt_x<* D' =+4 8?RCB?BCB#ppt_yB*Y3>B ppt_y<* D' =%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-s6Bwipe(left)*<3<*D' =%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-s6Bwipe(left)*<3<*+p+0+0 ++0+0 ++0  *(   x  c $D~PP ~ G  HR~_ж_ж? ,$D 0 Las soluciones de una ecuacin son los valores que pueden tomar las incgnitas de manera que, al sustituirlos en una ecuacin, la igualdad sea cierta. Dos ecuaciones son equivalentes si tienen la mismas soluciones. Transformaciones que conservan las soluciones de una ecuacin. Si se suma o resta el mismo nmero a los dos miembros de una ecuacin se obtiene una ecuacin equivalente. Si se multiplican o dividen los dos miembros de una ecuacin por un mismo nmero no nulo se obtiene una ecuacin equivalente lZZ  a(x   fW~_ж_ж?? l ,$D 0 = Ejemplos: Z   H j~_ж_жz ? <,$ 0 h La ecuacin 3x2  18x + 19 = 12x  29 tiene una solucin para x = 2. x = 1 no es solucin de la ecuacin anterior. Una ecuacin equivalente a la anterior es x2  10 x + 16 = 0 La ecuaciones x2 = 1 y x3 = 1 no son equivalentesZ  !  H  0@޽h ? ^WNff3""___PPT10"+vsD!' ~= @B D!' = @BA?%,( < +O%,( < +D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-s6Bwipe(left)*<3<* D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-s6Bwipe(left)*<3<* D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-s6Bwipe(left)*<3<* D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-s6Bwipe(left)*<3<* D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-s6Bwipe(left)*<3<* D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-s6Bwipe(left)*<3<* D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-s6Bwipe(left)*<3<* D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* F%(D' =-s6Bwipe(left)*<3<* FD' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* Fu%(D' =-s6Bwipe(left)*<3<* FuD' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* u%(D' =-s6Bwipe(left)*<3<* uD' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-s6Bwipe(left)*<3<* ++0+ 0 ++0+ 0 ++0+ 0 +IC0 P"H"45!(    c $ ~S<$D 0 ~   H,~_ж_ж?,$D 0 2Una ecuacin en la que slo aparecen polinomios se llama polinmica. Toda ecuacin polinmica se puede transformar en otra equivalente de la forma P(x) = 0, en donde P(x) es un polinomio. Se llama grado de la ecuacin al grado de P(x). Z(x  H ~_ж_жz ?[#,$ 0 lEcuaciones polinmicas de primer grado: toda ecuacin polinmica de primer grado se puede transformar en otra de la forma ax + b = 0 con a 02Z(dp /h  # #2,$D 0  Tȉ~_ж_жz ?/  @ Soluciones:  Z  N S     _h N  - c   h      T(~_ж_жz ? - c > b aZB   Z_ж_жDo?( $    T ~_ж_жz ?S i  `,esta ecuacin tiene una nica solucin: x = -Z-   H~_ж_жz ?,/@,$ 0 Interpretacin geomtrica: un polinomio de grado 1 est representado por una recta. La solucin de la ecuacin es la abcisa del punto de corte de la recta con el eje x$Z mh   # `#?,$D 0  #  # #  ,$D0~B  NZD1?   #  # # ,$D0~B  NZD1?l l  #  # # ,$D0~B  NZD1?D# D  "  # " ,$D0 " ~  # " ~ ,$D0\T " ~  # " ~ xB  HD1?"~ xB  HD1?"~ xB  HD1?"~ xB  HD1?J"J~ xB  HD1? " ~ xB  HD1? " ~ T H  # H ~B  NZD1?H H~B   NZD1? ~B ! NZD1?  ~B " NZD1?  ~B # NZD1?  ~B $ NZD1?K  K ~B % NZD1?  xB & HD1?~.~ xB ' HD1?"~ xB ( HD1?x xB ) HD1?>>l  (h  *# h  ,$D 0B +  `_ж_жDo?L h L B ,  `_ж_жDo?(P  -  `~_ж_жz jJ?   7OZ . T\~_ж_жz ?   7XZ / T~_ж_жz ?mcg 7YZ N _ 0# N ,$D0B 1B Z_ж_жDԔ?N ( {_ 2 T~_ж_жz ?   > y = ax + b Z .  O X 3#  ,$D 0 4 TL~_ж_ж? O 6 ,$D 0 F( b/a, 0) Z B 5B  `_ж_жDfԔ?q . XH  0@޽h ? ^WNff3  ___PPT10y .+µsDq' ~= @B D,' = @BA?%,( < +O%,( < +D' =%(DU' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D#' =+4 8?nCB!#ppt_x-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*D' =+4 8?\CB#ppt_hBCB#ppt_hB*Y3>B ppt_h<*D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-s6Bwipe(left)*<3<*D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-s6Bwipe(left)*<3<*D' =%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-s6Bwipe(left)*<3<*D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-s6Bwipe(left)*<3<* D' =%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-s6Bwipe(left)*<3<*D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*0%(D' =%(DH' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*3%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*3D#' =+4 8?nCB!#ppt_y-#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*3D' =+4 8?\CB#ppt_wBCB#ppt_wB*Y3>B ppt_w<*3D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*3++0+0 ++0+0 ++0+0 ++0+ 0 +40 D(    c $h~S<$D 0 ~ P  Ht~_ж_ж?Z,$D 0 Las ecuaciones polinmicas de segundo grado, tambin llamadas cuadrticas, son equivalentes a ecuaciones de la forma ax2 + bx + c = 0 con a 0ZZ> . (xK  T\~_ж_жz ?#K,$0 GSoluciones: estas ecuaciones pueden tener dos, una o ninguna solucin. 0HZ ;  H_ж_жz ?,$ 0 Interpretacin geomtrica: un polinomio de segundo grado est representado por una parbola. Segn la parbola corte al eje X en dos, uno o ningn punto la ecuacin cuadrtica tendr dos, una o ninguna solucin.$Z  H4_ж_ж? 8 ,$D0 <x2 + 1 = 0 tiene dos soluciones complejas: i. No tiene soluciones reales: la parbola no corta al eje x NjZ )=Y 7  # 7 ,$D0   # l_ж_жu""#!A ?z ?7 8 $D0   T_ж_ж?n Y y = x2 +14 Z /  c#   #  c# ,$D 0   # l_ж_ж^$)o*A ?z ? c#     T_ж_ж?7 c [ y = (x +2)24 Z    Z|_ж_ж??x  ]i,$D0 ^(x + 2)2 = 0 tiene una solucin doble:  2. El polinomio tiene una raz real doble. La parbola corta al eje x en un punto N{Z R  Z,"_ж_ж?? ;&,$D 0 \x2  2 = 0 tiene dos soluciones. El polinomio tiene dos races reales distintas. La parbola corta al eje x en dos puntos NzZ Z    #  ,$D  0  T_ж_жA ?z ?    T*_ж_ж? dy = x2  24 Z H  0@޽h ? ^WNff3  ___PPT10 .+;D' E= @B D' = @BA?%,( < +O%,( < +D' =%(DU' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D#' =+4 8?nCB!#ppt_x-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*D' =+4 8?\CB#ppt_hBCB#ppt_hB*Y3>B ppt_h<*D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-s6Bwipe(left)*<3<*DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*H%(D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-s6Bwipe(left)*<3<*DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-s6Bwipe(left)*<3<* DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-s6Bwipe(left)*<3<*++0+0 ++0+0 ++0+0 ++0+0 ++0+0 ++0+0 ++0+0 +0 V(    c $PS<$D 0    TQ_ж_жz ?#y j,$D0 X$Solucin de una ecuacin cuadrtica %Z%&  TW_ж_ж?w,$D0 nPara resolver ax2 + bx + c = 04Z   s *A ?s? YP8 $D0  s *A ?s? D8 $D0H  0@޽h ? ^WNff3yq___PPT10Q.+EpZD' d= @B D<' = @BA?%,( < +O%,( < +D' =%(DU' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D#' =+4 8?nCB!#ppt_x-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*D' =+4 8?\CB#ppt_hBCB#ppt_hB*Y3>B ppt_h<*D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D' =%(D' =%(D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D' =%(D' =%(D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*++0+0 ++0+0 ++0+0 +& 0 KCP 4(  4x 4 c $0T `)   4 c $A ?? N8 $D 0^ 4 By o?p,$D 0 Una solucin de este sistema: x = 3; y =  2. En este caso es nica DD 4 HA ? o?`V 8 $D0 4 Bo? D { ,$D 0 Interpretacin geomtrica: Cada igualdad del sistema representa una recta en el plano cartesiano. Una solucin de este sistema es un punto comn a ambas rectas  ,, 4 H o?mg,$D 0 =5x+y=13  4 H  o?)Tl# ,$D 0 ;x+y=13  4 No? c ,$D 0 D(3,  2)H 4 0@޽h ? ^WNff3.&___PPT10+OD' = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(DA' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*4%(D' =-}6B!slide(fromLeft)*<3<*4D' =%(D+' =%(D' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*4%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*4D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*4D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*4%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*4D' =+4 8?dCB0-#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*4D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*4%(D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*4%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*4D' =+4 8?dCB0-#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*4D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* 4%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<* 4D' =+4 8?dCB0-#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<* 4D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* 4%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<* 4D' =+4 8?dCB0-#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<* 4++0+40 ++0+40 ++0+40 ++0+ 40 ++0+ 40 + 0 `8}(  8x 8 c $ĚX`  W 8 Z_ж_жԔ?<,$D 0 YSistemas equivalentes: Dos sistemas son equivalentes cuando tienen las mismas soluciones$ZZEw 8 ZH_ж_жfԔ?  ,$D 0 ]Se pueden aplicar a un sistema las mismas transformaciones que a una ecuacin: Si se suma o se resta el mismo nmero a los dos miembros de una ecuacin de un sistema, se obtiene un sistema equivalente Si se multiplican o dividen los dos miembros de una ecuacin de un sistema por un mismo nmero distinto de cero, se obtiene un sistema equivalente2OZZMx 8 Z_ж_жԔ? ,$D 0 )Sistemas lineales y no lineales: Si en un sistema todas la ecuaciones son polinmicas de grado 1, se dice que es un sistema de ecuaciones lineales. En caso contrario se dice que el sistema es no lineal.2"ZZxH 8 0@޽h ? ^WNff3  ___PPT10 +L^D ' j= @B D ' = @BA?%,( < +O%,( < +D' =%(D' =%(D@' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*8%(D' =-o6Bbox(out)*<3<*8D' =%(D' =%(D@' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*8%(D' =-o6Bbox(out)*<3<*8D' =%(D' =%(D@' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*8%(D' =-o6Bbox(out)*<3<*8++0+80 ++0+80 ++0+80 +/ 0 p<R(  <x < c $h`   < c $A ??0!8 $D 0 < Bo?h b,$D 0 j"Es un sistema con solucin nica. ,#33 < c $A  ??*T 8  $D 0  < BXo?r l ,$D 0 dEs un sistema sin solucin. , 33 < c $A  ?? *8  $D 0  < Bo?] *W,$D  0 p(Es un sistema con infinitas soluciones. ,)33    <# t ,$D 0  < HA  ? o? 8  $D 0  < H o?!4 ? x + y = 1   3  < HX o?X  d A 5x + y = 13       <#   ,$D 0 < HA  ? o?  8  $D 0 < H  o?@O ? x + y = 1   3 < HP  o?0 g   ? x + y = 2     d <#   d,$D  0 < HA  ? o? d8  $D  0 < H  o?pR @  ? x + y = 1   3 < H$  o?   A 2x + 2y = 2   3H < 0@޽h ? ^WNff3  ___PPT10 +0dD' = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(D3' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*<%(D' =-o6Bwipe(up)*<3<*<D\' =%(D' =%(D' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<* <%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<* <D' =+4 8?\CB#ppt_hBCB#ppt_hB*Y3>B ppt_h<* <D' =%(D' =%(D@' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*<%(D' =-o6Bwipe(up)*<3<*<D' =%(D' =%(D3' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*<%(D' =-o6Bwipe(up)*<3<*<D\' =%(D' =%(D' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*<%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*<D' =+4 8?\CB#ppt_hBCB#ppt_hB*Y3>B ppt_h<*<D' =%(D' =%(D@' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*<%(D' =-o6Bwipe(up)*<3<*<D' =%(D' =%(D3' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*<%(D' =-o6Bwipe(up)*<3<*<D\' =%(D' =%(D' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*<%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*<D' =+4 8?\CB#ppt_hBCB#ppt_hB*Y3>B ppt_h<*<D' =%(D' =%(D@' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* <%(D' =-o6Bwipe(up)*<3<* <++0+<0 ++0+<0 ++0+ <0 +20  D2(  D D s *Y Z<$D 0    D c $A ??0 8 $D 0 D c $A ??0U 8 $D 0 D c $A ??0` 8 $D 0: D N] GW%HZ o?fV ,$D 0 R(1 ec) ( 2) + 2 ec (1 ec) ( 2) + 3 ec**33 D Na G H o?,~ L,$D 0 ^((2 ec) ( 1) + 3 ec332  D Z8e _ж_жԔ? J ,$D 0 t>La ecuacin 0 =  5 no puede satisfacerse y el sistema al que se ha llegado no tiene solucin. Como el sistema original es equivalente, tampoco tiene solucin.ZH D 0@޽h ?/ DD ^WNff3**___PPT10h*.+.[D`)' w = @B D)' = @BA?%,( < +O%,( < +D' =%(DU' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*D%(D#' =+4 8?nCB!#ppt_x-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*DD' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*DD' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*DD' =+4 8?\CB#ppt_hBCB#ppt_hB*Y3>B ppt_h<*DD' =%(D' =%(DA' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*D%(D' =-}6B!slide(fromLeft)*<3<*DD' =%(DU' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*D%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*DD#' =+4 8?nCB!#ppt_y+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*DD' =+4 8?\CB#ppt_wBCB#ppt_wB*Y3>B ppt_w<*DD' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*DD' =%(D' =%(DA' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*D%(D' =-}6B!slide(fromLeft)*<3<*DD' =%(DU' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*D%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*DD#' =+4 8?nCB!#ppt_y+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*DD' =+4 8?\CB#ppt_wBCB#ppt_wB*Y3>B ppt_w<*DD' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*DD' =%(DH' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*D%(D#' =+4 8?nCB!#ppt_x-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*DD' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*DD' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*DD' =+4 8?\CB#ppt_hBCB#ppt_hB*Y3>B ppt_h<*DD' =%(DA' =%(D' =A@BBB$B0B%(D' =1:Bvisible*o3>+B#style.visibility<* D%(Dc' =++4 8?CBa(6*min(max(#ppt_w*#ppt_h,.3),1)-7.4)/-.7*#ppt_wBCB#ppt_wB*Y3>B ppt_w<* DDc' =++4 8?CBa(6*min(max(#ppt_w*#ppt_h,.3),1)-7.4)/-.7*#ppt_hBCB#ppt_hB*Y3>B ppt_h<* DD' =+4 8?RCB?BCB#ppt_xB*Y3>B ppt_x<* DDk' =+34 8?CBi1+(6*min(max(#ppt_w*#ppt_h,.3),1)-7.4)/-.7*#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<* D++0+D0 ++0+D0 ++0+D0 ++0+ D0 + 70   H! (  H H s *d 8<$D 0    H c $A ??08 $D 0 H c $A ??P8 $D 0 H c $A ??8 $D 0: H Nl GW%H` o?C3 ,$D 0 R(1 ec) ( 2) + 2 ec (1 ec) ( 2) + 3 ec**33 H Z _ж_жԔ?PG,$D 0 uLa ecuacin 0 = 0 es siempre cierta y puede ser eliminada, obtenindose con ello un sistema equivalente al original. vZvu ..  H 0    : 2 `  H c $A" ?? 0    H 0ȗ    b x + y = 9 + 2z -3y = -14 - 8z! 2! ! H s *    MDejamos en el primer miembro, el mismo nmero de ecuaciones que de incgnitasN 2N N H 0  ` P  e#x = 9 + 2z - = y = $ 2$ $` H c $A ?? P   ` H c $A! ??   ` H c $A ??p F   H s *  P@ v$Al darle a z un valor cualquiera (por ejemplo z =  1), podemos obtener las otras incgnitas por sustitucin hacia arriba: y =2, x = 5. Ya tenemos una solucin: x= 5, y = 2, z =  1 Como a z se le puede dar cualquier valor concluimos que el sistema tiene infinitas soluciones.$Z H H 0@޽h ?H ^WNff3 ))___PPT10(.+/*D('  = @B D'' = @BA?%,( < +O%,( < +D' =%(DU' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*H%(D#' =+4 8?nCB!#ppt_x-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*HD' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*HD' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*HD' =+4 8?\CB#ppt_hBCB#ppt_hB*Y3>B ppt_h<*HD' =%(D' =%(DA' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*H%(D' =-}6B!slide(fromLeft)*<3<*HD' =%(DU' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*H%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*HD#' =+4 8?nCB!#ppt_y+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*HD' =+4 8?\CB#ppt_wBCB#ppt_wB*Y3>B ppt_w<*HD' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*HD' =%(D' =%(DA' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*H%(D' =-}6B!slide(fromLeft)*<3<*HD' =%(DH' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*H%(D#' =+4 8?nCB!#ppt_x-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*HD' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*HD' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*HD' =+4 8?\CB#ppt_hBCB#ppt_hB*Y3>B ppt_h<*HD}' =%(D%' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*H%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*HD' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*HD' =+4 8?RCB?BCB#ppt_xB*Y3>B ppt_x<*HD' =+4 8?RCB?BCB#ppt_yB*Y3>B ppt_y<*HD}' =%(D%' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*Hv%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*HvD' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*HvD' =+4 8?RCB?BCB#ppt_xB*Y3>B ppt_x<*HvD' =+4 8?RCB?BCB#ppt_yB*Y3>B ppt_y<*Hv++0+H0 ++0+H0 ++0+H0 +A0  L(  L L c $L  )<$D 0   t L HX _ж_ж?l,$D 0 No hay un mtodo general que permita resolver todos los sistema de ecuaciones no lineales. Pueden tener cualquier nmero de soluciones, en nmero finito o infinito. Las ecuaciones del sistema pueden representar rectas o curvas: resolverlo es encontrar todos los puntos en comn a las rectas  curvas que forman el sistemaBZB(x FA L# &- ,$D0 L HA ? o?FA  L Ht  o?C 5  L H  o?e_ 5 %  L <  o?v  ,$D0 =El sistema tiene dos soluciones: x = 3, y = 4 x = 4, y = 3,""  L <  o?@0,$D0 Estas soluciones corresponden a las coordenadas de los dos puntos en comn que tienen la circunferencia x2 + y2 = 25, y la recta x + y = 7X;33   E3   L# E3 ,$D0  L c $A ??E3 8 $D0  L  f _ж_жz Ԕ?H/ ;EjemploZ L Z _ж_жz Ԕ?7 ,$D 0 Se despeja y de la segunda ecuacin y se sustituye en la primera. Se obtiene: x2  7x + 12 = 0 Al resolver: x=3, x = 4 Sustituimos estos valores de x en la segunda ecuacin y se obtiene: y = 4, y = 34ZO xxH L 0@޽h ? ^WNff311___PPT101.+FW{DK0' )= @B D0' = @BA?%,( < +O%,( < +D' =%(DU' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*L%(D#' =+4 8?nCB!#ppt_x-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*LD' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*LD' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*LD' =+4 8?\CB#ppt_hBCB#ppt_hB*Y3>B ppt_h<*LD' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*L%(D' =-s6Bwipe(left)*<3<*LD' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*L[%(D' =-s6Bwipe(left)*<3<*L[D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*L[%(D' =-s6Bwipe(left)*<3<*L[D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*LB%(D' =-s6Bwipe(left)*<3<*LBD4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* L%(D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*LB%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*LBD' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*LBD{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*LB_%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*LB_D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*LB_D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*L_w%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*L_wD' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*L_wD{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*Lw%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*LwD' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*LwD' =%(D' =%(DV' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* L%(D' =-6B)randombar(vertical)*<3<* LD' =%(D' =%(DV' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* L%(D' =-6B)randombar(vertical)*<3<* LD4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*L%(++0+L0 ++0+L0 ++0+ L0 ++0+ L0 ++0+L0 +H40 PP(  Px P c $) )  P H")_ж_ж?S,$D 0 F Una inecuacin es una desigualdad entre dos expresiones en la que aparecen nmeros y letras ligados por operaciones. Las desigualdades pueden ser de cualquiera de los tipos: >, <, , o Las letras representan cantidades indeterminadas, y se llaman incgnitas. Las soluciones de una inecuacin son los valores que pueden tomar las incgnitas de manera que, al sustituirlos en la inecuacin, la desigualdad sea cierta .dZ O x^" P C x0$)_ж_жdo? p ,$D0 23x2  18x + 19 > 12x  294Z( (( '  P# p x ,$D 0N   P  2 P T_ж_ж Ԕ? B  P # l_ж_жDA)?    P T0)_ж_ж?'  = Incgnita Z     P# Rv Z ,$D 0N    P  2  P T_ж_ж Ԕ? B P # l_ж_жDA)?   P T6)_ж_ж?  ? Desigualdad Z   m  P#   Y,$D 0r P T_ж_жz Ԕ? 0  P T;)_ж_жz ? + m  Y 1er miembro2 Z      P#  k,$D 0r P T_ж_жz Ԕ? '  P TA)_ж_жz ?D   X 2o miembro2 Z ( H P 0@޽h ? ^WNff3""___PPT10"+!D="' I)= @B D!' = @BA?%,( < +O%,( < +D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*P%(D' =-s6Bwipe(left)*<3<*PD' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*P%(D' =-s6Bwipe(left)*<3<*PD' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*P%(D' =-s6Bwipe(left)*<3<*PD' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*P%(D' =-s6Bwipe(left)*<3<*PDA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*P%(D' =%(DH' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*P%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*PD#' =+4 8?nCB!#ppt_y+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*PD' =+4 8?\CB#ppt_wBCB#ppt_wB*Y3>B ppt_w<*PD' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*PDp' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* P%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<* PD' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<* PD' =+4 8?RCB?BCB#ppt_xB*Y3>B ppt_x<* PD' =+4 8?RCB?BCB#ppt_yB*Y3>B ppt_y<* PD' =%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*P%(D' =-s6Bwipe(left)*<3<*PD' =%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*P%(D' =-s6Bwipe(left)*<3<*P+p+0+P0 ++0+P0 +((0 `T(  Tx T c $ 12x  29 tiene una solucin para x = 1. x = 2 no es solucin de la inecuacin anterior. Una inecuacin equivalente a la anterior es x2  10 x + 16 > 0NZ  H T 0@޽h ? ^WNff3___PPT10+vsD' )= @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*T%(D' =-s6Bwipe(left)*<3<*TD' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*TB%(D' =-s6Bwipe(left)*<3<*TBD' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*TB%(D' =-s6Bwipe(left)*<3<*TBD' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*T%(D' =-s6Bwipe(left)*<3<*TD' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*Tv%(D' =-s6Bwipe(left)*<3<*TvD' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*Tv%(D' =-s6Bwipe(left)*<3<*TvD' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*T%(D' =-s6Bwipe(left)*<3<*TD' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*TH%(D' =-s6Bwipe(left)*<3<*THD' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*THy%(D' =-s6Bwipe(left)*<3<*THyD' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*Ty%(D' =-s6Bwipe(left)*<3<*Ty++0+T0 ++0+T0 ++0+T0 +A0 5-pX(  Xx X c $)PTY )  X HL)_ж_ж?/@,$D 0 ^Una desigualdad entre polinomios de primer grado es una inecuacin de primer grado. Puede ocurrir que: Se satisfagan para cualquier valor de la variable. No tengan solucin. Las que no estn en ninguno de los casos anteriores son equivalentes a inecuaciones de la forma: x < a, x > a, x a, o x a VgZZg (x X  fP)_ж_ж??dSLK ,$D 0 = Ejemplos: Z L X  fĦ)_ж_жz Ԕ? /dh ,$0 42x + 3 < 5x + 2 x > 1/3 2Z   D  X#  D ,$D 0B X  f_ж_жDԔ?  B  X  f_ж_жDԔ?D D D   m    X# m  ,$D02  X Z_ж_жԔ? q    X  f)_ж_жz Ԕ? m T  91/3ZH t    X# t  ,$D 0B X  `_ж_жD3Ԕ?t    X  fX)_ж_жz Ԕ?w  (Soluciones: (1/3,+)>Z333L X  f)_ж_жz Ԕ? x ,$ 0 43  2x < 5  2x 0 < 2 2Z X Z)_ж_жz Ԕ?% g ,$  0 $Como esto es siempre cierto, son son solucin todos los nmeros reales. Soluciones: ( ,+)P]ZV3333d X  fX)_ж_жz Ԕ? /,$  0 25  3x 2  3x 3 0 LZ O X  f)_ж_жz Ԕ? hr,$  0 ;Como esto es siempre falso, la inecuacin no tiene solucin.<Z;33H X 0@޽h ? ^WNff3 ..___PPT10-+t:\D=,' )= @B D+' = @BA?%,( < +O%,( < +D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*X%(D' =-s6Bwipe(left)*<3<*XD' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*XT%(D' =-s6Bwipe(left)*<3<*XTD' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*XTg%(D' =-s6Bwipe(left)*<3<*XTgD' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*Xg%(D' =-s6Bwipe(left)*<3<*XgD' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*X%(D' =-s6Bwipe(left)*<3<*XD' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*X0%(D' =-s6Bwipe(left)*<3<*X0D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*X%(D' =-s6Bwipe(left)*<3<*XDA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*X%(D' =%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*X%(D' =-s6Bwipe(left)*<3<*XD4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* X%(D' =%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* X%(D' =-s6Bwipe(left)*<3<* XD' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*X%(D' =-s6Bwipe(left)*<3<*XD' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*X]%(D' =-s6Bwipe(left)*<3<*X]D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*X%(D' =-s6Bwipe(left)*<3<*XD' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*X<%(D' =-s6Bwipe(left)*<3<*X<++0+X0 ++0+X0 ++0+X0 ++0+X0 ++0+X0 ++0+X0 ++0+X0 +0N0 "l(   l l Z 3f11?< l 0LM5 #c0 JINICIO(2 Z l B$d@޽h @ ? ̙33 0 x(  xX x C t   ~ x S \~t 0y  ~  H x 0޽h彖 ? 3380___PPT10.o@ 0 |(  |X | C t    | S N~t 0y    H | 0޽h彖 ? 3380___PPT10.o 0 (  X  C t     S ~t 0y    H  0޽h彖 ? 3380___PPT10.o@ 0 (  X  C t     S ~t 0y    H  0޽h彖 ? 3380___PPT10.op 0 (  X  C t     S Mt 0y    H  0޽h彖 ? 3380___PPT10.o: 0  (  X  C t     S mt 0y    H  0޽h彖 ? 3380___PPT10.o@  0 (  X  C t     S t 0y    H  0޽h彖 ? 3380___PPT10.o`  0 (  X  C t     S 0t 0y    H  0޽h彖 ? 3380___PPT10.o;  0 (  X  C t     S ' t 0y    H  0޽h彖 ? 3380___PPT10.oP馭 0 (  X  C t     S  t 0y    H  0޽h彖 ? 3380___PPT10.ok 0 (  X  C t     S  t 0y    H  0޽h彖 ? 3380___PPT10.o ǭ 0 (  X  C t   )  S  )t 0y  )  H  0޽h彖 ? 3380___PPT10.o¯ 0 (  X  C t   )  S 4X)t 0y  )  H  0޽h彖 ? 3380___PPT10.o 0 (  X  C t   )  S p)t 0y  )  H  0޽h彖 ? 3380___PPT10.o3 0 (  X  C t   )  S T)t 0y  )  H  0޽h彖 ? 3380___PPT10.oP 0 `(  X  C t   5  S T5t 0y  5  H  0޽h彖 ? 3380___PPT10.o#jx pUy>$].@H\!^OO!!ƀǏ!fc;S;&8gLBZ7ߩn3Vm}={\08ug0{߷{vR1SEԅ\mh!/+קϏUǔ&xm@,J9Jb(S*THH^ՏR1JS@@JQ4JRJPFpJ#(4hJՔP48J(T]Ϗ+;Vo/<λPpc1 ' \osh<h!LmWWyT8d>rJ?:ѩ)Jƾamv䯮_ov3ߗGH>B&Db};Htu'ھ;k[wܳsļvo6mۦłV {릪?_7> >˾;'ox{T%}U)ew.%~^%VT|{uv$Z:vK'<ՙh(rJ^{"~>82,KutYjp99EџƯ)m)-QaFȡv  S=QjHv9Y|3ҕp"wsf +g!}S`J=-w$}*+4Uy꣗Jw3h+c̫EVv=,t^ A6H_qɒt* l7|xrcjގk?+#OXlXݵɾqü뒶=_uTNӪy,u-mI9גwUV^[KAsS]{;ҭCp55-@Pl +]6̥Kcޱ!<=|0WKCԢ>"5s=ᨊDܯ'(%=98siOVߖذwv֝ɣM' @8&px/4 9*w$ew--SHVm<%]fԗa/oPyf%QBb;B.}:84vާ<9ԇ;z67 8i9a^z)/|zδ{?FJV]F[(iYXL]:  ON.rAe*o}r9;\Ŗ񥺟M X@P7HWH21Lm9|wND$9?>X_G^:O861ʭ&yRR(۾8q%?>mݗ(:LqogK"R9Wx+k?(822ƕgL.~DT".X.8MEV"΃mG[llΊspn]n;/IxW1ʹ)LD2^!kNO%v԰T#C顢2j8rY\+_QjSR-!Sr xRm59 d|ANuj4};{C-SaƜ#p*Idԍn.J|QfVP]ȸ*K])(}( G__E̤…Ybut}cEoQE(>/2J->ea=(# g2, ea(Ն^(c}4 Wς-P*s8(~El>ϓP=yx(MdPk{N@2V~ eeJN;P&Aze2P(S<2\PeBAXgRl'P\i (3ޅ"k)J;YP CmXGPCgXeaJ3Cλ,FPK߁H.30,rJa9 Rr6e( ˢ0,;PVs2,Ǡ6,ưea:r!"(meQ6@'c8Pq&(@ &Pڡ EbX.aXӰ\e+A9/`4Ϟxwc엏 ʦ$UOv-Nr}o8 6}[?^wm(8IIn)=|Yu}xfӕOu}1㼃1cύv}gu(HvWLQ<{8W\?̦MQƴ!g :j-s}*jGBɻR9M{.ZԘygQ??ʘ&W<2 (2 < JF3?ʈ'%SB5xdLXW\.5WݿkP?#?G6m!G9DXf#ǰ#qf<#k51]A_?[:4cm!h/qM](I? 2ڋ \f-G'1JCl?^o1Sc1|{M4bc ?}b_|$?M~_W>NPFLjlUL6[g3N>jKv5s?cgd?%X,zu]CuԖu<ѹYscpCB)+NZ$M{є>ee/;o!ܔFcXhX}57k)^AJ{ }iWi =OphToA%*  ,k/*g_aЀ(D`J,Фġ`<š ` ~ 8 3!:XP/2XPO%XjTʡQ`7*'`z 0*'zPi2rԓ9ie8Ш(ϡ@ ,7*Grzjp8A: r+d0&98ب|!p1*GPO[rAX`Q9VԳ[J  P/ 38;48IޫIR?τ jT0VC Wxk j#37*6Zc QXFc*SV:gƫ`ܓT>6Ac&fxI<9C`65C3<4զ`v j3T0V|MVw:^qmDHX=g@Q0ziȡW0 S`[Ar8c. 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