To determine whether each ordered pair is a solution to the equation [tex]\(7x + 4y = -23\)[/tex], we substitute the values of [tex]\(x\)[/tex] and [tex]\(y\)[/tex] from each pair into the equation and check if the resulting expression is valid.
1. For the pair [tex]\((6, -7)\)[/tex]:
[tex]\[
7(6) + 4(-7) = 42 - 28 = 14
\][/tex]
Since [tex]\( 14 \neq -23 \)[/tex], [tex]\((6, -7)\)[/tex] is not a solution.
2. For the pair [tex]\((-5, 3)\)[/tex]:
[tex]\[
7(-5) + 4(3) = -35 + 12 = -23
\][/tex]
Since [tex]\( -23 = -23 \)[/tex], [tex]\((-5, 3)\)[/tex] is a solution.
3. For the pair [tex]\((-1, -4)\)[/tex]:
[tex]\[
7(-1) + 4(-4) = -7 - 16 = -23
\][/tex]
Since [tex]\( -23 = -23 \)[/tex], [tex]\((-1, -4)\)[/tex] is a solution.
4. For the pair [tex]\((2, 6)\)[/tex]:
[tex]\[
7(2) + 4(6) = 14 + 24 = 38
\][/tex]
Since [tex]\( 38 \neq -23 \)[/tex], [tex]\((2, 6)\)[/tex] is not a solution.
So, the proper table should be:
\begin{tabular}{|c|c|c|}
\hline
[tex]\(\ (x, y) \)[/tex] & Yes & No \\
\hline
(6, -7) & & ✓ \\
\hline
(-5, 3) & ✓ & \\
\hline
(-1, -4) & ✓ & \\
\hline
(2, 6) & & ✓ \\
\hline
\end{tabular}
