Let's determine which pair of equations the point [tex]\((-3, 2)\)[/tex] is a solution to.
We are given four pairs of equations:
1. [tex]\(2x + 4y = -2\)[/tex] and [tex]\(-2x + 2y = 10\)[/tex]
2. [tex]\(2x + 4y = 2\)[/tex] and [tex]\(-2x + 2y = 10\)[/tex]
3. [tex]\(2x + 4y = -2\)[/tex] and [tex]\(-2x + 2y = -10\)[/tex]
4. [tex]\(2x + 4y = 2\)[/tex] and [tex]\(-2x + 2y = -10\)[/tex]
Let's test each pair to see if the point [tex]\((-3, 2)\)[/tex] satisfies both equations in any of the pairs.
### Checking Pair 1:
Equations:
[tex]\[2x + 4y = -2\][/tex]
[tex]\[-2x + 2y = 10\][/tex]
Substitute [tex]\((x, y) = (-3, 2)\)[/tex]:
[tex]\[2(-3) + 4(2) = -6 + 8 = 2\text{ (This is not equal to -2, so the first equation is not satisfied.)}\][/tex]
Therefore, [tex]\((-3, 2)\)[/tex] does not satisfy the first pair.
### Checking Pair 2:
Equations:
[tex]\[2x + 4y = 2\][/tex]
[tex]\[-2x + 2y = 10\][/tex]
Substitute [tex]\((x, y) = (-3, 2)\)[/tex]:
[tex]\[2(-3) + 4(2) = -6 + 8 = 2\text{ (The first equation is satisfied.)}\][/tex]
[tex]\[-2(-3) + 2(2) = 6 + 4 = 10\text{ (The second equation is satisfied.)}\][/tex]
Therefore, [tex]\((-3, 2)\)[/tex] satisfies both equations in the second pair.
### Checking Pair 3:
Equations:
[tex]\[2x + 4y = -2\][/tex]
[tex]\[-2x + 2y = -10\][/tex]
Substitute [tex]\((x, y) = (-3, 2)\)[/tex]:
[tex]\[2(-3) + 4(2) = -6 + 8 = 2\text{ (This is not equal to -2, so the first equation is not satisfied.)}\][/tex]
Therefore, [tex]\((-3, 2)\)[/tex] does not satisfy the third pair.
### Checking Pair 4:
Equations:
[tex]\[2x + 4y = 2\][/tex]
[tex]\[-2x + 2y = -10\][/tex]
Substitute [tex]\((x, y) = (-3, 2)\)[/tex]:
[tex]\[2(-3) + 4(2) = -6 + 8 = 2\text{ (The first equation is satisfied.)}\][/tex]
[tex]\[-2(-3) + 2(2) = 6 + 4 = 10\text{ (This is not equal to -10, so the second equation is not satisfied.)}\][/tex]
Therefore, [tex]\((-3, 2)\)[/tex] does not satisfy the fourth pair.
After checking all pairs of equations, we find that the point [tex]\((-3, 2)\)[/tex] is a solution to the second pair of equations:
[tex]\[2x + 4y = 2\][/tex]
[tex]\[-2x + 2y = 10\][/tex]
Thus, the point [tex]\((-3, 2)\)[/tex] is a solution to the second pair of equations.
