# How do you solve the system of equations: y = -3x + 5 and 5x - 4y = -3?

Aug 7, 2015

$\left(x , y\right) = \left(1 , 2\right)$

#### Explanation:

[1]$\textcolor{w h i t e}{\text{XXXX}}$$y = - 3 x + 5$
[2]$\textcolor{w h i t e}{\text{XXXX}}$$5 x - 4 y = - 3$

Since [1] gives us an expression for $y$ in terms of $x$
the obvious solution method would be to substitute this expression for $y$ in [2]
[3]$\textcolor{w h i t e}{\text{XXXX}}$5x-4(-3x+5)=-3#

Simplifying the left side
[4]$\textcolor{w h i t e}{\text{XXXX}}$$17 x - 20 = - 3$

[5]$\textcolor{w h i t e}{\text{XXXX}}$$17 x = 17$
[6]$\textcolor{w h i t e}{\text{XXXX}}$$x = 1$
Substituting $1$ for $x$ back in [1]
[7]$\textcolor{w h i t e}{\text{XXXX}}$$y = - 3 \left(1\right) + 5$
[8]$\textcolor{w h i t e}{\text{XXXX}}$$y = 2$