# How do you solve the system of linear equations 4x+3y= -2 and 2x-2y= -8?

Jul 30, 2018

$x = - 2 \mathmr{and} y = 2$

#### Explanation:

Here ,

color(red)(4x+3y=-2.....to(1)

color(red)(2x-2y=-8.....to(2)

Dividing both sides of $e q n . \left(2\right)$ by $2$

color(red)(x-y=-4

=>color(red)(x=y-4.....to(3)

Subst. value of $x$ into $\left(1\right)$ we get

$4 \left(y - 4\right) + 3 y = - 2$

$\implies 4 y - 16 + 3 y = - 2$

$\implies 4 y + 3 y = 16 - 2$

$\implies 7 y = 14$

=>color(blue)(y=2

Subst. $y = 2$ into $\left(3\right)$

color(blue)(x=2-4=-2

Hence, $x = - 2 \mathmr{and} y = 2$

Jul 30, 2018

$x = - 2$ and $y = 2$

#### Explanation:

$2 \cdot \left(2 x - 2 y\right) - \left(4 x + 3 y\right) = 2 \cdot \left(- 8\right) - \left(- 2\right)$

$4 x - 4 y - 4 x - 3 y = - 16 + 2$

$- 7 y = - 14$

Hence $y = \frac{- 14}{- 7} = 2$

So,

$2 x - 2 \cdot 2 = - 8$

$2 x - 4 = - 8$

$2 x = - 4$

Consequently, $x = \frac{- 4}{2} = - 2$