# How do you find the solution of the system of equations 2x – y = 4  and 3x + y = 1 ?

May 2, 2015

We can add the two equations to eliminate $y$

Adding the 2 equations will give us:

$\left(2 x - y\right) + \left(3 x + y\right) = 4 + 1$

$2 x - \cancel{y} + 3 x + \cancel{y} = 5$

$5 x = 5$

Dividing both sides by 5 gives us

$\frac{\cancel{5} x}{\cancel{5}} = \frac{\cancel{5}}{\cancel{5}}$

color(green)(x = 1

Now we can substitute $x = 1$ in the second equation to get $y$

$3 \cdot 1 + y = 1$

$3 + y = 1$

Subtracting 3 from both sides will give us:

$\cancel{3} + y - \cancel{3} = 1 - 3$

 color(green)(y = -2

The solution to these system of equations is:

color(green)(x = 1 ; y = -2