# How do you solve 3x + y = 2 and 4x + y = 20 using substitution?

Mar 14, 2018

$\left(x , y\right) = \left(18 , - 52\right)$

#### Explanation:

Given
[1]$\textcolor{w h i t e}{\text{XXX}} 3 x + y = 2$
[2]$\textcolor{w h i t e}{\text{XXX}} 4 x + y = 20$

We can re-arrange [1] into the form:
[3]$\textcolor{w h i t e}{\text{XXX}} y = 2 - 3 x$

Then we can substitute (as requested) $\left(2 - 3 x\right)$ for $y$ in [2]
[4]$\textcolor{w h i t e}{\text{XXX}} 4 x + \left(2 - 3 x\right) = 20$

Simplifying [4]
[5]$\textcolor{w h i t e}{\text{XXX}} x + 2 = 20$

The subtracting $2$ from both sides of [5]
[6]$\textcolor{w h i t e}{\text{XXX}} x = 18$

Based on [6], we can now substitute $18$ for $x$ in [1]
[7]$\textcolor{w h i t e}{\text{XXX}} 3 \cdot 18 + y = 2$

With some simplification
[8]$\textcolor{w h i t e}{\text{XXX}} 54 + y = 2$

[9]$\textcolor{w h i t e}{\text{XXX}} y = - 52$