This worksheet provides eight practice problems for students to solve systems of linear equations using the elimination method.

Let’s solve each system of equations using elimination. We’ll go one by one, step by step.

---

Problem 1:

Equations:
- -2x - 3y = -7
- -2x - 5y = -5

Step 1: Subtract the second equation from the first to eliminate x.

(-2x - 3y) - (-2x - 5y) = -7 - (-5)

→ -2x - 3y + 2x + 5y = -7 + 5

→ 2y = -2 → y = -1

Step 2: Plug y = -1 into one of the original equations. Let’s use the first:

-2x - 3(-1) = -7 → -2x + 3 = -7 → -2x = -10 → x = 5

✔ Solution: (5, -1)

---

Problem 2:

Equations:
- -5x + 3y = 10
- -5x - 2y = 35

Step 1: Subtract the second equation from the first.

(-5x + 3y) - (-5x - 2y) = 10 - 35

→ -5x + 3y + 5x + 2y = -25

→ 5y = -25 → y = -5

Step 2: Plug y = -5 into first equation:

-5x + 3(-5) = 10 → -5x -15 = 10 → -5x = 25 → x = -5

✔ Solution: (-5, -5)

---

Problem 3:

Equations:
- x + 2y = -1
- x + y = 2

Step 1: Subtract the second equation from the first.

(x + 2y) - (x + y) = -1 - 2

→ x + 2y - x - y = -3 → y = -3

Step 2: Plug y = -3 into second equation:

x + (-3) = 2 → x = 5

✔ Solution: (5, -3)

---

Problem 4:

Equations:
- -3x - 3y = 12
- 5x - 3y = 20

Step 1: Subtract the first equation from the second to eliminate y.

(5x - 3y) - (-3x - 3y) = 20 - 12

→ 5x - 3y + 3x + 3y = 8 → 8x = 8 → x = 1

Step 2: Plug x = 1 into first equation:

-3(1) - 3y = 12 → -3 - 3y = 12 → -3y = 15 → y = -5

✔ Solution: (1, -5)

---

Problem 5:

Equations:
- -5x - 4y = 8
- 4x - 4y = -28

Step 1: Subtract the second equation from the first.

(-5x - 4y) - (4x - 4y) = 8 - (-28)

→ -5x - 4y - 4x + 4y = 36 → -9x = 36 → x = -4

Step 2: Plug x = -4 into second equation:

4(-4) - 4y = -28 → -16 - 4y = -28 → -4y = -12 → y = 3

✔ Solution: (-4, 3)

---

Problem 6:

Equations:
- 4x + 2y = -12
- -5x + 2y = 6

Step 1: Subtract the second equation from the first.

(4x + 2y) - (-5x + 2y) = -12 - 6

→ 4x + 2y + 5x - 2y = -18 → 9x = -18 → x = -2

Step 2: Plug x = -2 into first equation:

4(-2) + 2y = -12 → -8 + 2y = -12 → 2y = -4 → y = -2

✔ Solution: (-2, -2)

---

Problem 7:

Equations:
- 3x + 4y = -12
- -3x - 2y = 12

Step 1: Add the two equations together to eliminate x.

(3x + 4y) + (-3x - 2y) = -12 + 12

→ 0x + 2y = 0 → 2y = 0 → y = 0

Step 2: Plug y = 0 into first equation:

3x + 4(0) = -12 → 3x = -12 → x = -4

✔ Solution: (-4, 0)

---

Problem 8:

Equations:
- -5x + 5y = 0
- 5x + 4y = 0

Step 1: Add the two equations to eliminate x.

(-5x + 5y) + (5x + 4y) = 0 + 0

→ 0x + 9y = 0 → 9y = 0 → y = 0

Step 2: Plug y = 0 into first equation:

-5x + 5(0) = 0 → -5x = 0 → x = 0

✔ Solution: (0, 0)

---

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