# Is (5, -1) a solution to this system of equations: 3x+6y = 9 and -2x-y = -6 ?

Jan 19, 2017

No. See below, the second equation is not solve therefore this point is not a solution for this set of equations.

#### Explanation:

To determine if this point is a solution to the system of equations we need to substitute the point into each equation and see if it solves the equation.

We will substitute $\textcolor{red}{5}$ for $\textcolor{red}{x}$ and $\textcolor{b l u e}{- 1}$ for $\textcolor{b l u e}{y}$

Then $3 \textcolor{red}{x} + 6 \textcolor{b l u e}{y} = 9$ becomes:

$\left(3 \times \textcolor{red}{5}\right) + \left(6 \times \textcolor{b l u e}{- 1}\right) = 9$

$15 - 6 = 9$

$9 = 9$

And $- 2 \textcolor{red}{x} - \textcolor{b l u e}{y} = - 6$ becomes:

$\left(- 2 \times \textcolor{red}{5}\right) - \left(\textcolor{b l u e}{- 1}\right) = - 6$

$- 10 + = - 6$

$- 9 \ne - 6$

Because the second equation is not solve this point is not a solution for this set of equations.