Question

In the following exercises, determine if the following points are solutions to the given system of equations.

$\left\{\begin{array}{l}-3x+y=8\\ -x+2y=-9\end{array}\right.$

$\begin{array}{l}\left(\mathrm{a}\right)\left(-5,-7\right)\\ \left(\mathrm{b}\right)\left(-5,7\right)\end{array}$

Short answer

Part (a) The ordered pair, $(-5,-7)$is a solution of the system of linear equations.

Part (b) The ordered pair $(-5,7)$is not a solution to the system of linear equations.

Step-by-step solution

Part (a) Step 1. Given information.

Given the system of equations$\left\{\begin{array}{l}-3x+y=8\\ -x+2y=-9\end{array}\right.$

Part (a) Step 2. Checking the values for the first equation.

Substituting the value in the equation,$-3x+y=8$, we get,

$\begin{array}{r}-3x+y=8\\ -3(-5)+(-7)=8\\ 15-7=8\\ 8=8\end{array}$

Part (a) Step 3. Checking the values for the second equation. 

Substituting the value, we get

$\begin{array}{rcl}-x+2y& =& -9\\ -(-5)+2(-7)& =& -9\\ 5-14& =& -9\\ -9& =& -9\end{array}$

Part (b) Step 1. Checking the values for the first equation.

Substituting the values, we get

$\begin{array}{r}-3x+y=8\\ -3(-5)+\left(7\right)=8\\ 15+7=8\\ 22=8\end{array}$

Part (b) Step 2. Checking the values for the second equation.

Substituting the values, we get,

$\begin{array}{r}-x+2y=-9\\ -(-5)+2\left(7\right)=-9\\ 5+14=-9\\ 19=-9\end{array}$

Part (b) Step 3. Conclusion.

The point $\left(-5,7\right)$does not satisfy the given system of equations.