# How do you find the solution of the system of equations 3x - 5y = 13 and x - 2y = 5?

May 18, 2015

Isolate one variable in one equation and then substitute the value of it in the other.

Let's isolate $x$ in the second equation and then substitute its value in the first.

$x = 5 + 2 y$

$3 \left(5 + 2 y\right) - 5 y = 13$
$15 + 6 y - 5 y = 13$
$y = - 2$

As $x = 5 + 2 y$, then $x = 5 + 2 \left(- 2\right) = 1$

So, $y = - 2$ and $x = 1$