In this multiple choice question, we want to determine which option gives us a solution of (1,6).
The quickest way to do this is to test the point in each equation. We know
[tex](1,6)\rightarrow(x,y),[/tex]so we can simply substitute the value of x and y into each set to see if they both make the equations true.
Option A:
We are given the equations:
[tex]\begin{gathered} y=-5x-1 \\ \\ y=-x+7 \end{gathered}[/tex]Substituting the point (1,6) into the first equation gives us:
[tex]\begin{gathered} 6=-5(1)-1 \\ \\ 6=-6 \end{gathered}[/tex]This is already a false equation, so Option A is not correct.
Option B:
We have
[tex]\begin{gathered} y=5x+1 \\ \\ y=x-7 \end{gathered}[/tex]We will substitute into the first equation:
[tex]\begin{gathered} 6=5(1)+1 \\ \\ 6=6 \end{gathered}[/tex]The first equation works. Now, let's try the second equation:
[tex]\begin{gathered} 6=1-7 \\ \\ 6=-6 \end{gathered}[/tex]Unfortunately, that is a false statement, so Option B is not our answer.
Option C:
The equations are
[tex]\begin{gathered} y=5x+1 \\ \\ y=-x-7 \end{gathered}[/tex]From the previous question, we know the first equation is true. For the second equation, we have
[tex]\begin{gathered} 6=-1-7 \\ \\ 6=-7 \end{gathered}[/tex]This is false.
Option D:
Through process of elimination, this is the correct answer. However, let's prove it.
We know the first equation worked, so let's try the second:
[tex]\begin{gathered} 6=-1+7 \\ 6=6 \end{gathered}[/tex]The correct answer is Option D.
[tex]\begin{gathered} y=5x+1 \\ \\ y=-x+7 \end{gathered}[/tex]
