# How do you solve the following system using substitution?: y=x-5, y=2x

Oct 24, 2015

$x = - 5$
$y = - 10$

#### Explanation:

You simply have to substitute $x$ or $y$ from the first equation to $x$ or $y$ in the second equation.

So in the first equation, the value of $y$ is $x - 5$. You just have to substitute this value into $y$ in the second equation.

$\left[1\right] \textcolor{w h i t e}{X X} y = 2 x$

$\left[2\right] \textcolor{w h i t e}{X X} x - 5 = 2 x$

$\left[3\right] \textcolor{w h i t e}{X X} - 5 = 2 x - x$

$\left[4\right] \textcolor{w h i t e}{X X} \textcolor{b l u e}{x = - 5}$

Now that we have the value of $x$, we can plug it into either of the two equations to solve for $y$.

$\left[1\right] \textcolor{w h i t e}{X X} y = x - 5$

$\left[2\right] \textcolor{w h i t e}{X X} y = \left(- 5\right) - 5$

$\left[3\right] \textcolor{w h i t e}{X X} \textcolor{red}{y = - 10}$