To determine which of the ordered pairs satisfy the linear equation [tex]\(5x = 3y - 18\)[/tex], we need to substitute each pair [tex]\((x, y)\)[/tex] into the equation and see if the equation holds true.
Let's evaluate each pair one by one:
Pair (a): [tex]\((-1, 1)\)[/tex]
Substitute [tex]\(x = -1\)[/tex] and [tex]\(y = 1\)[/tex] into the equation:
[tex]\[5(-1) = 3(1) - 18\][/tex]
[tex]\[ -5 = 3 - 18\][/tex]
[tex]\[ -5 \neq -15 \][/tex]
This pair does not satisfy the equation.
Pair (b): [tex]\((-1, 3)\)[/tex]
Substitute [tex]\(x = -1\)[/tex] and [tex]\(y = 3\)[/tex] into the equation:
[tex]\[5(-1) = 3(3) - 18\][/tex]
[tex]\[ -5 = 9 - 18\][/tex]
[tex]\[ -5 \neq -9 \][/tex]
This pair does not satisfy the equation.
Pair (c): [tex]\((-3, 1)\)[/tex]
Substitute [tex]\(x = -3\)[/tex] and [tex]\(y = 1\)[/tex] into the equation:
[tex]\[5(-3) = 3(1) - 18\][/tex]
[tex]\[ -15 = 3 - 18\][/tex]
[tex]\[ -15 = -15 \][/tex]
This pair satisfies the equation.
Pair (d): [tex]\((3, -1)\)[/tex]
Substitute [tex]\(x = 3\)[/tex] and [tex]\(y = -1\)[/tex] into the equation:
[tex]\[5(3) = 3(-1) - 18\][/tex]
[tex]\[ 15 = -3 - 18\][/tex]
[tex]\[ 15 \neq -21 \][/tex]
This pair does not satisfy the equation.
So, the ordered pair that satisfies the linear equation [tex]\(5x = 3y - 18\)[/tex] is:
[tex]\[
\boxed{(-3, 1)}
\][/tex]
