To determine which ordered pair is a solution to the equation [tex]\(2x - y = 9\)[/tex], we need to substitute each pair into the equation and check if it satisfies the equation.
Let’s go through each option step-by-step:
Option A: [tex]\((-4, 1)\)[/tex]
- Substitute [tex]\(x = -4\)[/tex] and [tex]\(y = 1\)[/tex] into the equation:
[tex]\[
2(-4) - 1 = -8 - 1 = -9 \neq 9
\][/tex]
This pair does not satisfy the equation.
Option B: [tex]\((-2, 5)\)[/tex]
- Substitute [tex]\(x = -2\)[/tex] and [tex]\(y = 5\)[/tex] into the equation:
[tex]\[
2(-2) - 5 = -4 - 5 = -9 \neq 9
\][/tex]
This pair does not satisfy the equation.
Option C: [tex]\((5, 1)\)[/tex]
- Substitute [tex]\(x = 5\)[/tex] and [tex]\(y = 1\)[/tex] into the equation:
[tex]\[
2(5) - 1 = 10 - 1 = 9
\][/tex]
This pair satisfies the equation.
Option D: [tex]\((6, -3)\)[/tex]
- Substitute [tex]\(x = 6\)[/tex] and [tex]\(y = -3\)[/tex] into the equation:
[tex]\[
2(6) - (-3) = 12 + 3 = 15 \neq 9
\][/tex]
This pair does not satisfy the equation.
Therefore, the ordered pair that is a solution to the equation [tex]\(2x - y = 9\)[/tex] is [tex]\((5, 1)\)[/tex], which corresponds to option C.
