# How do you solve the following linear system: -x + 4y = -8 , 3x - 5y = 3 ?

Jun 15, 2018

$x = - 4$ and $y = - 3$.

#### Explanation:

Equation 1

$- x + 4 y = - 8$

Equation 2

$3 x - 5 y = 3$

First solve Equation 1 for $x$.

Equation 3

$x = 4 y + 8$

Substitute the expression for $x$ from Equation 3 into Equation 2.

$3 \left(4 y + 8\right) - 5 y = 3$

Apply the distributive property

$12 y + 24 - 5 y = 3$

Combine like terms

$7 y = - 21$

Divide both sides of this equation by 7.

$y = - 3$

Substitute this value for $y$ into Equation 3 to determine the value of $x$.

$x = 4 \left(- 3\right) + 8 = - 12 + 8 = - 4$