Math worksheet for solving systems of equations using elimination or substitution.

Let’s solve each system step by step. I’ll use substitution or elimination — whichever is easier for each pair.

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

Since both equal y, set them equal:
2x - 3 = x - 1
Subtract x from both sides:
x - 3 = -1
Add 3 to both sides:
x = 2

Now plug into y = x - 1 → y = 2 - 1 = 1

✔ Check:
First equation: y = 2(2) - 3 = 4 - 3 = 1 ✔️
Second: y = 2 - 1 = 1 ✔️

→ x = 2, y = 1

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

Set equal:
-2x + 1 = 2x + 3
Add 2x to both sides:
1 = 4x + 3
Subtract 3:
-2 = 4x
Divide by 4:
x = -0.5 or -1/2

Plug into y = 2x + 3 → y = 2(-0.5) + 3 = -1 + 3 = 2

✔ Check:
First: y = -2(-0.5) + 1 = 1 + 1 = 2 ✔️
Second: y = 2(-0.5) + 3 = -1 + 3 = 2 ✔️

→ x = -1/2, y = 2

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Problem 3:
4x - 2y = 8
2x + 2y = 4

Use elimination — add the two equations (the -2y and +2y cancel):
(4x + 2x) + (-2y + 2y) = 8 + 4
6x = 12 → x = 2

Plug into second equation: 2(2) + 2y = 4 → 4 + 2y = 4 → 2y = 0 → y = 0

✔ Check:
First: 4(2) - 2(0) = 8 - 0 = 8 ✔️
Second: 2(2) + 2(0) = 4 + 0 = 4 ✔️

→ x = 2, y = 0

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Problem 4:
-2x - y = -2
2x + 4y = 11

Add the two equations (eliminate x):
(-2x + 2x) + (-y + 4y) = -2 + 11
0x + 3y = 9 → y = 3

Plug into first equation: -2x - 3 = -2 → -2x = 1 → x = -1/2

✔ Check:
First: -2(-0.5) - 3 = 1 - 3 = -2 ✔️
Second: 2(-0.5) + 4(3) = -1 + 12 = 11 ✔️

→ x = -1/2, y = 3

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Problem 5:
6x + 2y = 10
3x + 3y = -13

Let’s simplify first equation by dividing by 2:
3x + y = 5 → so y = 5 - 3x

Plug into second equation:
3x + 3(5 - 3x) = -13
3x + 15 - 9x = -13
-6x + 15 = -13
-6x = -28
x = 28/6 = 14/3 ≈ 4.666... Wait — let me check again.

Wait — maybe better to eliminate.

Multiply second equation by 2:
6x + 6y = -26

Now subtract first equation:
(6x + 6y) - (6x + 2y) = -26 - 10
4y = -36 → y = -9

Now plug into first: 6x + 2(-9) = 10 → 6x - 18 = 10 → 6x = 28 → x = 28/6 = 14/3

But that’s messy — let me double-check original problem.

Original:
6x + 2y = 10
3x + 3y = -13

Try multiplying second by 2: 6x + 6y = -26
Subtract first: (6x+6y) - (6x+2y) = -26 - 10 → 4y = -36 → y = -9 ✔️
Then 6x + 2(-9) = 10 → 6x = 28 → x = 14/3

Yes, it’s correct even if fractional.

✔ Check:
First: 6*(14/3) + 2*(-9) = 28 - 18 = 10 ✔️
Second: 3*(14/3) + 3*(-9) = 14 - 27 = -13 ✔️

→ x = 14/3, y = -9

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Problem 6:
7x - 12y = -13
5x + 4y = 19

Let’s eliminate y. Multiply second equation by 3:
15x + 12y = 57

Now add to first:
(7x + 15x) + (-12y + 12y) = -13 + 57
22x = 44 → x = 2

Plug into second: 5(2) + 4y = 19 → 10 + 4y = 19 → 4y = 9 → y = 9/4

✔ Check:
First: 7(2) - 12*(9/4) = 14 - 27 = -13 ✔️
Second: 5(2) + 4*(9/4) = 10 + 9 = 19 ✔️

→ x = 2, y = 9/4

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Problem 7:
4x + 2y = 14
7x - 3y = -8

Simplify first equation: divide by 2 → 2x + y = 7 → y = 7 - 2x

Plug into second:
7x - 3(7 - 2x) = -8
7x - 21 + 6x = -8
13x = 13 → x = 1

Then y = 7 - 2(1) = 5

✔ Check:
First: 4(1) + 2(5) = 4 + 10 = 14 ✔️
Second: 7(1) - 3(5) = 7 - 15 = -8 ✔️

→ x = 1, y = 5

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Problem 8:
15x + 3y = 9
10x + 7y = -4

Simplify first equation: divide by 3 → 5x + y = 3 → y = 3 - 5x

Plug into second:
10x + 7(3 - 5x) = -4
10x + 21 - 35x = -4
-25x = -25 → x = 1

Then y = 3 - 5(1) = -2

✔ Check:
First: 15(1) + 3(-2) = 15 - 6 = 9 ✔️
Second: 10(1) + 7(-2) = 10 - 14 = -4 ✔️

→ x = 1, y = -2

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Final Answer:

1. x = 2, y = 1
2. x = -1/2, y = 2
3. x = 2, y = 0
4. x = -1/2, y = 3
5. x = 14/3, y = -9
6. x = 2, y = 9/4
7. x = 1, y = 5
8. x = 1, y = -2