To determine which of the given ordered pairs is a solution to the equation [tex]\(6x - 4y = 4\)[/tex], we need to substitute each pair into the equation and check if it satisfies the equation.
Let's check each pair step-by-step:
1. Pair [tex]\((-2, -4)\)[/tex]:
[tex]\[
6(-2) - 4(-4) = -12 + 16 = 4
\][/tex]
The left side equals [tex]\(4\)[/tex], which is the right side of the equation. Therefore, [tex]\((-2, -4)\)[/tex] is a solution.
2. Pair [tex]\((-1, 0)\)[/tex]:
[tex]\[
6(-1) - 4(0) = -6 + 0 = -6
\][/tex]
The left side equals [tex]\(-6\)[/tex], which is not equal to [tex]\(4\)[/tex]. Therefore, [tex]\((-1, 0)\)[/tex] is not a solution.
3. Pair [tex]\((5, 4)\)[/tex]:
[tex]\[
6(5) - 4(4) = 30 - 16 = 14
\][/tex]
The left side equals [tex]\(14\)[/tex], which is not equal to [tex]\(4\)[/tex]. Therefore, [tex]\((5, 4)\)[/tex] is not a solution.
4. Pair [tex]\((2, -2)\)[/tex]:
[tex]\[
6(2) - 4(-2) = 12 + 8 = 20
\][/tex]
The left side equals [tex]\(20\)[/tex], which is not equal to [tex]\(4\)[/tex]. Therefore, [tex]\((2, -2)\)[/tex] is not a solution.
After checking all the pairs, we find that the pair [tex]\((-2, -4)\)[/tex] is the only one that satisfies the equation [tex]\(6x - 4y = 4\)[/tex].
Thus, the ordered pair that is a solution to the equation [tex]\(6x - 4y = 4\)[/tex] is [tex]\((-2, -4)\)[/tex].
