Algebra worksheet for solving systems of equations by elimination.

Let’s solve each system of equations by elimination. We’ll go one at a time, showing the steps clearly.

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Problem 1:
-4x - 2y = -12
4x + 8y = -24

Add the two equations to eliminate x:
(-4x + 4x) + (-2y + 8y) = -12 + (-24)
→ 0x + 6y = -36
→ y = -6

Plug y = -6 into first equation:
-4x - 2(-6) = -12
-4x + 12 = -12
-4x = -24
x = 6

✔ Solution: (6, -6)

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Problem 2:
4x + 8y = 20
-4x + 2y = -30

Add the equations to eliminate x:
(4x - 4x) + (8y + 2y) = 20 + (-30)
→ 0x + 10y = -10
→ y = -1

Plug y = -1 into first equation:
4x + 8(-1) = 20
4x - 8 = 20
4x = 28
x = 7

✔ Solution: (7, -1)

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Problem 3:
x - y = 11
2x + y = 19

Add the equations to eliminate y:
(x + 2x) + (-y + y) = 11 + 19
→ 3x = 30
→ x = 10

Plug x = 10 into first equation:
10 - y = 11
-y = 1
y = -1

✔ Solution: (10, -1)

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Problem 4:
-6x + 5y = 1
6x + 4y = -10

Add the equations to eliminate x:
(-6x + 6x) + (5y + 4y) = 1 + (-10)
→ 0x + 9y = -9
→ y = -1

Plug y = -1 into first equation:
-6x + 5(-1) = 1
-6x - 5 = 1
-6x = 6
x = -1

✔ Solution: (-1, -1)

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Problem 5:
-2x - 9y = -25
-4x - 9y = -23

Subtract the first equation from the second to eliminate y:
(-4x - (-2x)) + (-9y - (-9y)) = -23 - (-25)
→ -2x + 0y = 2
→ -2x = 2
→ x = -1

Plug x = -1 into first equation:
-2(-1) - 9y = -25
2 - 9y = -25
-9y = -27
y = 3

✔ Solution: (-1, 3)

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Problem 6:
8x + y = -16
-3x + y = -5

Subtract the second equation from the first to eliminate y:
(8x - (-3x)) + (y - y) = -16 - (-5)
→ 11x = -11
→ x = -1

Plug x = -1 into first equation:
8(-1) + y = -16
-8 + y = -16
y = -8

✔ Solution: (-1, -8)

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

Subtract the second equation from the first:
(-6x - (-6x)) + (6y - 3y) = 6 - (-12)
→ 0x + 3y = 18
→ y = 6

Plug y = 6 into first equation:
-6x + 6(6) = 6
-6x + 36 = 6
-6x = -30
x = 5

✔ Solution: (5, 6)

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Problem 8:
7x + 2y = 24
8x + 2y = 30

Subtract first equation from second:
(8x - 7x) + (2y - 2y) = 30 - 24
→ x = 6

Plug x = 6 into first equation:
7(6) + 2y = 24
42 + 2y = 24
2y = -18
y = -9

✔ Solution: (6, -9)

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Problem 9:
5x + y = 9
10x - 7y = -18

Multiply first equation by 7 to make y coefficients opposites:
7*(5x + y) = 7*9 → 35x + 7y = 63

Now add to second equation:
35x + 7y = 63
10x - 7y = -18
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45x = 45 → x = 1

Plug x = 1 into first equation:
5(1) + y = 9 → y = 4

✔ Solution: (1, 4)

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Problem 10:
-4x + 9y = 9
x - 3y = -6

Multiply second equation by 4 to match x coefficient:
4*(x - 3y) = 4*(-6) → 4x - 12y = -24

Add to first equation:
-4x + 9y = 9
4x - 12y = -24
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0x - 3y = -15 → y = 5

Plug y = 5 into second original equation:
x - 3(5) = -6 → x - 15 = -6 → x = 9

✔ Solution: (9, 5)

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Problem 11:
-3x + 7y = -16
-9x + 5y = 16

Multiply first equation by 3 to match x coefficient:
3*(-3x + 7y) = 3*(-16) → -9x + 21y = -48

Subtract second equation from this:
(-9x + 21y) - (-9x + 5y) = -48 - 16
→ 0x + 16y = -64 → y = -4

Plug y = -4 into first equation:
-3x + 7(-4) = -16
-3x - 28 = -16
-3x = 12 → x = -4

✔ Solution: (-4, -4)

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Problem 12:
-7x + y = -19
-2x + 3y = -19

Multiply first equation by 3 to match y coefficient:
3*(-7x + y) = 3*(-19) → -21x + 3y = -57

Subtract second equation from this:
(-21x + 3y) - (-2x + 3y) = -57 - (-19)
→ -19x = -38 → x = 2

Plug x = 2 into first equation:
-7(2) + y = -19 → -14 + y = -19 → y = -5

✔ Solution: (2, -5)

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Final Answer:
1) (6, -6)
2) (7, -1)
3) (10, -1)
4) (-1, -1)
5) (-1, 3)
6) (-1, -8)
7) (5, 6)
8) (6, -9)
9) (1, 4)
10) (9, 5)
11) (-4, -4)
12) (2, -5)