# How do you solve 4x + y = 26 and 5x - 2y =13?

Jul 8, 2018

The solution is the point $\left(5 , 6\right)$.

#### Explanation:

Equation 1: $4 x + y = 26$

Equation 2: $5 x - 2 y = 13$

We can use addition/elimination and substitution to solve this system.

Multiply Equation 1 by $2$.

$2 \left(4 x + y\right) = 26 \times 2$

Simplify.

$8 x + 2 y = 52$

$8 x + 2 y = 52$
$5 x - 2 y = 13$
$- - - - -$
$13 x$$\textcolor{w h i t e}{\ldots \ldots .} = 65$

Divide both sides by $13$.

$x = \frac{65}{13}$

$x = 5$

Substitute $5$ for $x$ in Equation 2 and solve for $y$.

$5 \left(5\right) - 2 y = 13$

$25 - 2 y = 13$

Subtract $25$ from both sides.

$- 2 y = 13 - 25$

$- 2 y = - 12$

Divide both sides by $- 2$.

$y = \frac{- 12}{- 2}$ $\leftarrow$ Two negatives make a positive.

$y = 6$

The solution is the point $\left(5 , 6\right)$.

graph{(4x+y-26)(5x-2y-13)=0 [-9.33, 10.67, 0.08, 10.08]}