# How do solve the following linear system?:  3x – 4y = 7, x-y=2 ?

May 16, 2018

$\left(x , y\right) = \left(+ 1 , - 1\right)$

#### Explanation:

Given
[1]$\textcolor{w h i t e}{\text{XXX}} 3 x - 4 y = 7$
[2]$\textcolor{w h i t e}{\text{XXX}} x - y = 2$

There are several ways to solve this but since it was asked under "Systems Using Substitution", we will approach it that way:

Rearrange [2] into an equation in terms of $x$
[3]$\textcolor{w h i t e}{\text{XXX}} x = y + 2$

Now substitute $\left(y + 2\right)$ for $x$ in [1]
[4]$\textcolor{w h i t e}{\text{XXX}} 3 \left(y + 2\right) - 4 y = 7$

Expanding and simplifying [4]
[5]$\textcolor{w h i t e}{\text{XXX}} - y + 6 = 7$
or
[6]$\textcolor{w h i t e}{\text{XXX}} y = - 1$

Now substitute $\left(- 1\right)$ for $y$ back in [2] (or you could have used [1])
[7]$\textcolor{w h i t e}{\text{XXX}} x - \left(- 1\right) = 2$
Simplifying:
[8]$\textcolor{w h i t e}{\text{XXX}} x = 1$