# Is (2,5) a solution to the system of equations 6x + y = 17 and 3x + 2y = 16?

Mar 4, 2017

Because the pair is a solution for both equations it is therefore a solution for the system of equations.

#### Explanation:

First, substitute $2$ for $x$ and $5$ for $y$ in the first equation and determine if this pair is a solution:

$6 x + y = 17$ becomes:

$\left(6 \times 2\right) + 5 = 17$

$12 + 5 = 17$

$17 = 17$

Because the pair is a solution for the first equation we must do the same substitution and solution for the second equation:

$3 x + 2 y = 16$ becomes:

$\left(3 \times 2\right) + \left(2 \times 5\right) = 16$

$6 + 10 = 16$

$16 = 16$