# How do you solve the following system: 4x+3y= -1 , x-y=3 ?

Apr 3, 2018

$x = \frac{8}{7} \text{ or " 1 1/7color(white)("xxxx")y=-13/7" or } - 1 \frac{6}{7}$

#### Explanation:

Given
[1]$\textcolor{w h i t e}{\text{XXX}} 4 x + 3 y = - 1$
[2]$\textcolor{w h i t e}{\text{XXX}} x - y = 3$

Re-arranging [2]
[3]$\textcolor{w h i t e}{\text{XXX}} x = y + 3$

Substituting $\left(y + 3\right)$ for $x$ in [1]
[4]$\textcolor{w h i t e}{\text{XXX}} 4 \left(y + 3\right) + 3 y = - 1$

Expanding and simplifying the lefts side of [4]
[5]$\textcolor{w h i t e}{\text{XXX}} 7 y + 12 = - 1$

Subtracting $12$ from both sides of [5]
[6]$\textcolor{w h i t e}{\text{XXX}} 7 y = - 13$

Dividing both sides of [6] by 7
[8]$\textcolor{w h i t e}{\text{XXX}} y = - \frac{13}{7}$

Substituting $\left(- \frac{13}{7}\right)$ for $y$ in [3]
[9]$\textcolor{w h i t e}{\text{XXX}} x = - \frac{13}{7} + 3 = \frac{- 13 + 21}{7} = \frac{8}{7}$