# How do you solve 2x - y = 4 and 4x = 2y + 8?

Apr 7, 2015

Dividing both sides of the second equation by 2, we get

$\frac{4 x}{2} = \frac{2 y}{2} + \frac{8}{2}$

$2 x = y + 4$

$2 x - y = 4$

This is the same equation as the first one. It means that there are INFINITE solutions for $x$ and $y$.
Any values of x and y that satisfy the first equation will also satisfy the second one.

For eg. if we choose x = 2, y = 0:

First equation :
$2 x - y = 4$
$\left(2 \cdot 2\right) - 0 = 4$ (which is equal to the Right Hand Side)

Second equation :
$4 x = 2 y + 8$
Left Hand Side is $4 x = 4 \cdot 2 = 8$
And the Right Hand Side is $2 y + 8 = \left(2 \cdot 0\right) + 8 = 8$

Both the equations will be satisfied for various such values of $x \mathmr{and} y$ like (3,2); (4,6) and so on..