# How do you solve the system of equations 2x - 5y = - 1 and 4x - 5y = 13?

Apr 4, 2018

$\left(x , y\right) = \left(7 , 3\right)$

#### Explanation:

$2 x = 5 y - 1$
$x = \frac{5}{2} y - \frac{1}{2}$ solve for $x$ in terms of $y$ in the first equation
$4 \left(\frac{5}{2} y - \frac{1}{2}\right) - 5 y = 13$ plug into other equation
$10 y - 2 - 5 y = 13$ distribute
$5 y - 2 = 13$ combine like terms
$5 y = 15$
$y = 3$
Now, going back to the other equation
$2 x - 5 \left(3\right) = - 1$ plug in value of y
$2 x - 15 = - 1$
$2 x = 14$
$x = 7$