Question

For each ordered pair, determine whether it is a solution to 7x + 4y = -23(x,y) (2,6) it is a solution yes or no(-5,3) it is a solution yes or no(6-7) it is a solution yes or no(-1,-4) it is a solution yes or no

Answer 1

To do this, first plug the values of x and y into the given equation. If you get a true statement, the ordered pair will be a solution to the equation, otherwise, it won't.

So, for the ordered pair (2,6) you have

$\begin{gathered} 7x+4y=-23 \\ 7(2)+4(6)=-23 \\ 14+24=-23 \\ 38=-23 \end{gathered}$

Since the proposition is false, then the ordered pair (2,6) is not a solution to the equation.

For the ordered pair (-5,3) you have

$\begin{gathered} 7x+4y=-23 \\ 7(-5)+4(3)=-23 \\ -35+12=-23 \\ -23=-23 \end{gathered}$

Since the proposition is true, then the ordered pair (-5,3) is a solution to the equation.

For the ordered pair (6,-7) you have

$\begin{gathered} 7x+4y=-23 \\ 7(6)+4(-7)=-23 \\ 42-28=-23 \\ 14=-23 \end{gathered}$

Since the proposition is false, then the ordered pair (6,-7) is not a solution to the equation.

Finally, for the ordered pair (-1,-4) you have

$\begin{gathered} 7x+4y=-23 \\ 7(-1)+4(-4)=-23 \\ -7-16=-23 \\ -23=-23 \end{gathered}$

Since the proposition is true, then the ordered pair (-1,-4) is a solution to the equation.