Warrayat Instructional Unit - Free Printable

Let’s solve each system by elimination. I’ll go one by one, showing the steps clearly so you can follow along.

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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

✔ Answer: (6, -6)

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

Add them:
(4x - 4x) + (8y + 2y) = 20 - 30 → 10y = -10 → y = -1

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

✔ Answer: (7, -1)

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

Add them:
(x + 2x) + (-y + y) = 11 + 19 → 3x = 30 → x = 10

Plug into first: 10 - y = 11 → -y = 1 → y = -1

✔ Answer: (10, -1)

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

Add them:
(-6x + 6x) + (5y + 4y) = 1 - 10 → 9y = -9 → y = -1

Plug into second: 6x + 4(-1) = -10 → 6x - 4 = -10 → 6x = -6 → x = -1

✔ Answer: (-1, -1)

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

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

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

✔ Answer: (-1, 3)

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

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

Plug into second: -3(-1) + y = -5 → 3 + y = -5 → y = -8

✔ Answer: (-1, -8)

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

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

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

✔ Answer: (5, 6)

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

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

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

✔ Answer: (6, -9)

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

Multiply first equation by 7:
35x + 7y = 63

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

Plug into first: 5(1) + y = 9 → y = 4

✔ Answer: (1, 4)

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

Multiply second equation by 3:
3x - 9y = -18

Add to first:
-4x + 9y + 3x - 9y = 9 - 18 → -x = -9 → x = 9

Plug into second: 9 - 3y = -6 → -3y = -15 → y = 5

✔ Answer: (9, 5)

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

Multiply first equation by 3:
-9x + 21y = -48

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

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

✔ Answer: (-4, -4)

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

Multiply first equation by 3:
-21x + 3y = -57

Subtract second equation:
(-21x + 3y) - (-2x + 3y) = -57 - (-19)
→ -19x + 0 = -38 → x = 2

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

✔ Answer: (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)