Question

For each order pair, determine whether it is a solution to the system of equations.

Answer 1

A ordered pair is a solution to the system if it satisfies all the equations of the system.

We have to check each equation for each pair.

We start with (-9,-6):

`\begin{gathered} 7(-9)-4(-6)=8 \\ -63+24=8 \\ -39=8\longrightarrow\text{False} \end{gathered}`

As one of the equation is not satisfied, (-9,-6) is not a solution.

For (7,7) we have:

`\begin{gathered} 7(7)-4(7)=8 \\ 49-28=8 \\ 21=8\longrightarrow\text{False} \end{gathered}`

As one of the equation is not satisfied, (7,7) is not a solution.

For (0,-2) we have:

`\begin{gathered} 7(0)-4(-2)=8 \\ 0+8=8 \\ 8=8\longrightarrow\text{True} \end{gathered}`

As this equation is satisfied, we test the second equation:

`\begin{gathered} -2(0)+3(-2)=7 \\ 0-6=7 \\ -6=7\longrightarrow\text{False} \end{gathered}`

As one of the equations is false, (0,-2) is not a solution.

Now, we test (4,5):

`\begin{gathered} 7(4)-4(5)=8 \\ 28-20=8 \\ 8=8\longrightarrow\text{True} \end{gathered}`

As this equation is satisfied, we test the second equation:

`\begin{gathered} -2(4)+3(5)=7 \\ -8+15=7 \\ 7=7 \end{gathered}`

The ordered pair (4,5) is a solution to the system.

Answer:

The only pair that is a solution is (4,5)