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

Let’s solve each system of equations by graphing — but since we can’t actually draw here, we’ll check if the given solution point (the one written under each problem) works in both equations. If it does, then that point is where the two lines cross — and that’s the answer!

We’ll go one by one.

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Problem 1:
Equations:
- y = 4x - 10
- y = (1/3)x + 1
Given solution: (3, 2)

Check in first equation:
y = 4(3) - 10 = 12 - 10 = 2 → matches y=2 ✔

Check in second equation:
y = (1/3)(3) + 1 = 1 + 1 = 2 → matches y=2 ✔

So (3,2) is correct.

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Problem 2:
Equations:
- -5x + 4y = -16
- x + 4y = 8
Given solution: (4, 1)

Check first equation:
-5(4) + 4(1) = -20 + 4 = -16 → matches ✔

Check second equation:
4 + 4(1) = 4 + 4 = 8 → matches ✔

So (4,1) is correct.

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Problem 3:
Equations:
- -x + 3y = 6
- 4x + 3y = -9
Given solution: (-3, 1)

Check first equation:
-(-3) + 3(1) = 3 + 3 = 6 → matches ✔

Check second equation:
4(-3) + 3(1) = -12 + 3 = -9 → matches ✔

So (-3,1) is correct.

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Problem 4:
Equations:
- y = -(4/3)x - 3
- y = -(7/5)x - 3
Given solution: (0, -3)

Check first equation:
y = -(4/3)(0) - 3 = 0 - 3 = -3 → matches ✔

Check second equation:
y = -(7/5)(0) - 3 = 0 - 3 = -3 → matches ✔

So (0,-3) is correct.

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Problem 5:
Equations:
- -x + 2y = -6
- 3x + 2y = 2
Given solution: (2, -2)

Check first equation:
-(2) + 2(-2) = -2 - 4 = -6 → matches ✔

Check second equation:
3(2) + 2(-2) = 6 - 4 = 2 → matches ✔

So (2,-2) is correct.

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Problem 6:
Equations:
- -2x + 3y = -9
- x + y = 2
Given solution: (3, -1)

Check first equation:
-2(3) + 3(-1) = -6 - 3 = -9 → matches ✔

Check second equation:
3 + (-1) = 2 → matches ✔

So (3,-1) is correct.

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Problem 7:
Equations:
- y = -2x + 2
- y = (1/3)x - 5
Given solution: (3, -4)

Check first equation:
y = -2(3) + 2 = -6 + 2 = -4 → matches ✔

Check second equation:
y = (1/3)(3) - 5 = 1 - 5 = -4 → matches ✔

So (3,-4) is correct.

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Problem 8:
Equations:
- y = -(5/2)x + 10
- y = (1/2)x + 4
Given solution: (2, 5)

Check first equation:
y = -(5/2)(2) + 10 = -5 + 10 = 5 → matches ✔

Check second equation:
y = (1/2)(2) + 4 = 1 + 4 = 5 → matches ✔

So (2,5) is correct.

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All given solutions are correct! Each point satisfies both equations in its system.

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