# How do you solve by substitution 0.3x-0.2y=0.5 and x-2y= -5?

Jun 15, 2015

By simplifying and re-arranging the terms, we get
$\left(x , y\right) = \left(5 , 5\right)$

#### Explanation:

[1]$\textcolor{w h i t e}{\text{XXXX}}$$0.3 x - 0.2 y = 0.5$
[2]$\textcolor{w h i t e}{\text{XXXX}}$$x - 2 y = - 5$

I would suggest the first thing to do is to simplify [1] by multiplying everything by 10
[3]$\textcolor{w h i t e}{\text{XXXX}}$$3 x - 2 y = 5$

In order to use substitution, re-arrange [2] to isolate $x$
[3]$\textcolor{w h i t e}{\text{XXXX}}$$x = 2 y - 5$

Substitute $2 y - 5$ for $x$ in [3]
[4]$\textcolor{w h i t e}{\text{XXXX}}$$3 \left(2 y - 5\right) - 2 y = 5$
Simplify
[5]$\textcolor{w h i t e}{\text{XXXX}}$$4 y - 15 = 5$
[6]$\textcolor{w h i t e}{\text{XXXX}}$$y = 5$

Using [6], substitute $5$ for $y$ in [2]
[7]$\textcolor{w h i t e}{\text{XXXX}}$$x - 2 \left(5\right) = - 5$
[8]$\textcolor{w h i t e}{\text{XXXX}}$$x = 5$