2x+3y = 2
2x-3y = 12
Método de Igualación :
1 ) Se despeja a " y " en la ecuación " 2x-3y = 12 " :
2x-3y = 12
2x-3y-2x = 12-2x
-3y = 12-2x
-(-3y) = -(12-2x)
3y = 2x-12
(3/3)y = (2x-12)/3
y = (2/3)x-(12/3)
y = (2/3)x-4
2 ) Se despeja a " y " en la ecuación " 2x+3y = 2 " :
2x+3y = 2
2x+3y-2x = 2-2x
3y = 2-2x
(3/3)y = (2-2x)/3
y = (2/3)-(2/3)x
3 ) Se igualan las ecuaciones resultantes " y = (2/3)x-4 " e " y = (2/3)-(2/3)x " :
(2/3)x-4 = (2/3)-(2/3)x
(2/3)x-4+(2/3)x = (2/3)-(2/3)x+(2/3)x
2(2/3)x-4 = 2/3
(4/3)x-4 = 2/3
(4/3)x-4+4 = 2/3+4 ; 4 = 12/3
(4/3)x = 2/3+12/3
(4/3)x = (2+12)/3
(4/3)x = 14/3
(4/3)x×3/4 = 14/3×3/4
x = ((14×3)/(3×4))
x = 42/12
x = (42÷6)/(12÷6)
x = 7/2
4 ) Se reemplaza a " x = 7/2 " en la ecuación " y = (2/3)-(2/3)x " :
y = (2/3)-(2/3)(7/2)
y = (2/3)-((2×7)/(3×2))
y = (2/3)-(7/3)
y = (2-7)/3
y = - 5/3
5 ) Se verifica :
2(7/2)+(-5/3) = 2
7+(-5) = 2
7 - 5 = 2
2 = 2
2(7/2)-3(-5/3) = 12
7-(-5) = 12
7+5 = 12
12 = 12
.
R// Por ende , ( x , y ) = ( 7/2 , - 5/3 ) es el conjunto solución del anterior sistema lineal de ecuaciones .
