Question

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

Answer 1

The point `(2, 1)` IS a solution of the system of equations.

Explanation:

`x+3y = 5`

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

`2 + 3(1) = 5`

`2 + 3 = 5`

`5 = 5` Yes, it works.

Now let's test `3x + 2y = 8`:
`3(2) + 2(1) = 8`

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

Because the points work for both equations, we know that the point `(2, 1)` 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:
https://www.khanacademy.org/math/algebra/systems-of-linear-equations/introduction-to-systems-of-linear-equations/v/testing-a-solution-for-a-system-of-equations

Hope this helps!