# How do you solve 2x + y = 5 and  x + y = 4?

Mar 29, 2018

$\textcolor{b l u e}{x = 1}$ and $\textcolor{b l u e}{y = 3}$

#### Explanation:

$2 x + y = 5 \setminus \setminus \setminus \setminus \left[1\right]$

$x + y = 4 \setminus \setminus \setminus \setminus \setminus \setminus \left[2\right]$

Rearrange $\left[2\right]$ so y is in terms of $x$:

$y = 4 - x \setminus \setminus \setminus \left[3\right]$

Substitute $\left[3\right]$ into $\left[1\right]$:

$2 x + \left(4 - x\right) = 5$

$2 x + 4 - x = 5$

$x = 5 - 4 = 1$

Substitute this result into $\left[2\right]$:

$1 + y = 4$

$y = 4 - 1 = 3$

Result:

$\textcolor{b l u e}{x = 1}$ and $\textcolor{b l u e}{y = 3}$