To determine which ordered pairs are solutions to the equation [tex]\(3x + 3y = -x + 5y\)[/tex], we need to substitute the given points into the equation and verify if both sides of the equation are equal.
Let's start with the ordered pair [tex]\((1, 2)\)[/tex]:
1. Substitute [tex]\(x = 1\)[/tex] and [tex]\(y = 2\)[/tex] into the left-hand side of the equation:
[tex]\[
3x + 3y = 3(1) + 3(2) = 3 + 6 = 9
\][/tex]
2. Now substitute [tex]\(x = 1\)[/tex] and [tex]\(y = 2\)[/tex] into the right-hand side of the equation:
[tex]\[
-x + 5y = -(1) + 5(2) = -1 + 10 = 9
\][/tex]
Since the left-hand side [tex]\(9\)[/tex] equals the right-hand side [tex]\(9\)[/tex], the pair [tex]\((1, 2)\)[/tex] is a solution to the equation.
Next, let's check the ordered pair [tex]\((2, 4)\)[/tex]:
1. Substitute [tex]\(x = 2\)[/tex] and [tex]\(y = 4\)[/tex] into the left-hand side of the equation:
[tex]\[
3x + 3y = 3(2) + 3(4) = 6 + 12 = 18
\][/tex]
2. Now substitute [tex]\(x = 2\)[/tex] and [tex]\(y = 4\)[/tex] into the right-hand side of the equation:
[tex]\[
-x + 5y = -(2) + 5(4) = -2 + 20 = 18
\][/tex]
Since the left-hand side [tex]\(18\)[/tex] equals the right-hand side [tex]\(18\)[/tex], the pair [tex]\((2, 4)\)[/tex] is a solution to the equation.
Based on this analysis, both [tex]\((1, 2)\)[/tex] and [tex]\((2, 4)\)[/tex] are solutions to the equation [tex]\(3x + 3y = -x + 5y\)[/tex].
Therefore, the correct answer is:
(c) Both [tex]\((1, 2)\)[/tex] and [tex]\((2, 4)\)[/tex]
