42.4k views
4 votes
For each order pair, determine whether it is a solution to the system of equations.

For each order pair, determine whether it is a solution to the system of equations-example-1
User Nekman
by
7.8k points

1 Answer

5 votes

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)

User Lpaseen
by
8.6k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories