# Is (2, 1) a solution to this system of equations? x + 3y = 5 3x + 2y = 8

Apr 14, 2018

The point $\left(2 , 1\right)$ IS a solution of the system of equations.

#### Explanation:

$x + 3 y = 5$

To see if $\left(2 , 1\right)$ is a solution of the system of equations, we plug in the point into both equations. Let's plug it into $x + 3 y = 5$ first:
$x + 3 y = 5$

$2 + 3 \left(1\right) = 5$

$2 + 3 = 5$

$5 = 5$ Yes, it works.

Now let's test $3 x + 2 y = 8$:
$3 \left(2\right) + 2 \left(1\right) = 8$

$6 + 2 = 8$ Yes, it works again.

Because the points work for both equations, we know that the point $\left(2 , 1\right)$ IS a solution of the system of equations.

For more information on checking if something is a solution to a system of equations, check this khan academy video: