# How do you solve the system y=x-1 and x+y=3 using substitution?

Jan 20, 2017

$x = 2$ and $y = 1$

#### Explanation:

$y = x - 1$
$x + y = 3$

In the second equation, substitute $y$ with its value from the first equation, $\textcolor{red}{\left(x - 1\right)}$.

$x + y = 3$

$x + \textcolor{red}{\left(x - 1\right)} = 3$

Open the brackets and simplify.

$x + \textcolor{red}{x - 1} = 3$

$2 x - 1 = 3$

Add $1$ to each side.

$2 x = 4$

Divide both sides by $2$.

$x = 2$

In the first equation, substitute $x$ with $\textcolor{b l u e}{2}$.

$y = x - 1$

$y = \textcolor{b l u e}{2} - 1$

$y = 1$