# How do you solve x + y = 2 and 2x + y = -1 using substitution?

Mar 7, 2016

$x = - 3 \mathmr{and} y = 5$

#### Explanation:

Since $x + y = 2$, we can say that $x = 2 - y$.

We then substitute this into the equation $2 x + y = - 1$.

So it becomes $2 \left(2 - y\right) + y = - 1$.

Open the bracket and simplify.

$4 - 2 y + y = - 1$

$4 - y = - 1$

Add $\left(1 + y\right)$ to both sides of the equation and simplify.

$4 - y + \left(1 + y\right) = - 1 + \left(1 + y\right)$

$4 \cancel{- y} + \left(1 + \cancel{y}\right) = \cancel{- 1} + \left(\cancel{1} + y\right)$

$5 = y$

Substitute the value of $y$ back in the first equation.

$x = 2 - y$

$= 2 - 5$

$= - 3$

So we have $x = - 3$ and $y = 5$. To check your answer. Substitute both values into both equations.

$x + y = - 3 + 5 = 2$

$2 x + y = 2 \left(- 3\right) + 5 = - 1$

They match.