How do solve the following linear system?: $- 2 x + 3 y = - 19, x + 2 y = 2$ $-2x + 3y = -19 , x+2y =2$ ?

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Answer 1 · 2016-01-13T16:04:42

The solution for the system of equations is
$x = \frac{44}{7}, y = - \frac{15}{7}$ $color(blue)(x=44/7, y=-15/7$

$- 2 x + 3 y = - 19$ $color(blue)(-2x) +3y = -19$ .........equation $(1)$ $(1)$

$x + 2 y = 2$ $x + 2y = 2$ , multiplying by $2$ $2$
$2 x + 4 y = 4$ $color(blue)(2x) + 4y = 4$ .......................equation $(2)$ $(2)$

Solving by elimination

Adding equations $1$ $1$ and $2$ $2$

$cancelcolor(blue)(-2x) +3y = -19$

$cancelcolor(blue)(2x) + 4y = 4$

$7y = -15$

$color(blue)(y = -15/7$

Finding $x$ from equation $2$
$x + 2y = 2$

$x = 2- 2y$

$x = 2- 2 xx (-15/7)$

$x = 2 +30/7$

$x = 14/7 +30/7$

$color(blue)(x = 44/7$

How do solve the following linear system?: -2x + 3y = -19 , x+2y =2 −2x+3y=−19,x+2y=2-2x + 3y = -19 , x+2y =2 ?