# How do you solve the simultaneous equations y = 3x and  x + 2y =21?

Jul 13, 2015

Since we are given an expression for $y$ as one of the equations, the simplest way to solve this pair of equations is through substitution.
$\left(x , y\right) = \left(3 , 9\right)$

#### Explanation:

[1]$\textcolor{w h i t e}{\text{XXXX}}$$y = 3 x$
[2]$\textcolor{w h i t e}{\text{XXXX}}$$x + 2 y = 21$

Based on [1], we can replace $y$ with $3 x$ in [2], giving
[3]$\textcolor{w h i t e}{\text{XXXX}}$$x + 2 \left(3 x\right) = 21$
Simplifying:
[4]$\textcolor{w h i t e}{\text{XXXX}}$$7 x = 21$
or
[5]$\textcolor{w h i t e}{\text{XXXX}}$$x = 3$

Based on [5], we can replace $x$ with $3$ in [1], giving
[6]$\textcolor{w h i t e}{\text{XXXX}}$$y = 3 \left(3\right)$
or
[7]$\textcolor{w h i t e}{\text{XXXX}}$$y = 9$