Solve each system of linear equations by graphing on the provided coordinate planes.

I'll solve each system of linear equations step by step.

Problem 1:
2x + 3y = -6
-2x + 3y = 6

Adding the two equations:
(2x + 3y) + (-2x + 3y) = -6 + 6
6y = 0
y = 0

Substituting y = 0 into the first equation:
2x + 3(0) = -6
2x = -6
x = -3

Solution: (-3, 0)

Problem 2:
-2x + 3y = -9
x + y = 2

From the second equation: x = 2 - y

Substituting into the first equation:
-2(2 - y) + 3y = -9
-4 + 2y + 3y = -9
5y = -5
y = -1

Then: x = 2 - (-1) = 3

Solution: (3, -1)

Problem 3:
-x + 3y = 6
4x + 3y = -9

Subtracting the first from the second:
(4x + 3y) - (-x + 3y) = -9 - 6
5x = -15
x = -3

Substituting x = -3 into the first equation:
-(-3) + 3y = 6
3 + 3y = 6
3y = 3
y = 1

Solution: (-3, 1)

Problem 4:
-x + 3y = 6
-5x + 3y = 6

Subtracting the first from the second:
(-5x + 3y) - (-x + 3y) = 6 - 6
-4x = 0
x = 0

Substituting x = 0 into the first equation:
-(0) + 3y = 6
3y = 6
y = 2

Solution: (0, 2)

Problem 5:
-5x + 4y = -16
x + 4y = 8

Subtracting the second from the first:
(-5x + 4y) - (x + 4y) = -16 - 8
-6x = -24
x = 4

Substituting x = 4 into the second equation:
4 + 4y = 8
4y = 4
y = 1

Solution: (4, 1)

Problem 6:
2x + y = 2
-x + y = -4

Subtracting the second from the first:
(2x + y) - (-x + y) = 2 - (-4)
3x = 6
x = 2

Substituting x = 2 into the first equation:
2(2) + y = 2
4 + y = 2
y = -2

Solution: (2, -2)

Problem 7:
5x + 3y = 12
-x + 3y = -6

Subtracting the second from the first:
(5x + 3y) - (-x + 3y) = 12 - (-6)
6x = 18
x = 3

Substituting x = 3 into the second equation:
-(3) + 3y = -6
-3 + 3y = -6
3y = -3
y = -1

Solution: (3, -1)

Problem 8:
-x + 2y = -6
3x + 2y = 2

Subtracting the first from the second:
(3x + 2y) - (-x + 2y) = 2 - (-6)
4x = 8
x = 2

Substituting x = 2 into the first equation:
-(2) + 2y = -6
-2 + 2y = -6
2y = -4
y = -2

Solution: (2, -2)

Final Answer:
1) (-3, 0)
2) (3, -1)
3) (-3, 1)
4) (0, 2)
5) (4, 1)
6) (2, -2)
7) (3, -1)
8) (2, -2)