Question

Решите систему линейных уравнений: {2(4x-y)+3(4x+y)=32. {5(4x-y)-2(4x+y)=4

Answer 1

$\left \{ {2(4x-y)+3(4x+y)=32} \atop {5(4x-y)-2(4x+y)=4}} \right.$

1)
$2(4x-y)+3(4x+y)=32$
$8x-2y+12x+3y=32$
$20x+y=32$

2)
$5(4x-y)-2(4x+y)=4$
$20x-5y-8x-2y=4$
$12x-7y=4$

$\left \{ {{20x+y=32} \atop {12x-7y=4}} \right. \left \{ {{y=32-20x} \atop {12x-7y=4}} \right.$

$12x-7(32-20x)=4$
$12x-224+140x=4$
$-128x=228$
$x= -\frac{228}{128}$
$x= -\frac{57}{32}$
$x= -1\frac{25}{32}$

$y=32-20* (-1\frac{25}{32} )$
$y = 32+ \frac{285}{8}$
$y=32+35 \frac{5}{8}$
$y=67 \frac{5}{8}$

Ответ: $-1 \frac{25}{32};67 \frac{5}{8}$