# How do you solve the system of equations 2y = 10x + 24 and 5x - y = - 12?

May 8, 2018

There are infinitely many solutions,

#### Explanation:

Make $y$ the subject in both equations:

$2 y = 10 x + 24 \text{ and } 5 x - y = - 12$

$y = 5 x + 12 \textcolor{w h i t e}{\times \times \times \times} 5 x + 12 = y$

We can see now that the two equations are actually exactly the same.

There is no unique solution for an equation with two variables.
The equations cannot be solved.

A few solutions are:

$x = 1 , \text{ } y = 17$
$x = 0 , \text{ } y = 12$
$x = 3 , \text{ } y = 27$
$x = - 5 , \text{ } y = - 13$