Year 12 Simultaneous Equations Worksheet — Level 3 — Answers
Answer sheet with worked solutions for the Year 12 simultaneous equations worksheet.
Year 12 · Mathematics · Simultaneous Equations
Year 12 Simultaneous Equations Worksheet — Level 3 — Answers
Success Tutoring
Solve each pair of equations. Check your solution satisfies both equations.
1.Solve simultaneously: 4x − 3y = 10 and 2x − y = 4
Answer: x = 1, y = −2
- Multiply equation 1 by 2 and equation 2 by 4 to match the x coefficients
- 8x − 6y = 20 and 8x − 4y = 16
- Subtract: −2y = 4, so y = −2
- Substitute back: x = 1
2.Solve simultaneously: 2x + y = −12 and 3x + 3y = −24
Answer: x = −4, y = −4
- Multiply equation 1 by 3 and equation 2 by 2 to match the x coefficients
- 6x + 3y = −36 and 6x + 6y = −48
- Subtract: −3y = 12, so y = −4
- Substitute back: x = −4
3.Solve simultaneously: 2x + 3y = 7 and 3x − 4y = 2
Answer: x = 2, y = 1
- Multiply equation 1 by 3 and equation 2 by 2 to match the x coefficients
- 6x + 9y = 21 and 6x − 8y = 4
- Subtract: 17y = 17, so y = 1
- Substitute back: x = 2
4.Solve simultaneously: 2x − 4y = 24 and 5x + 5y = −15
Answer: x = 2, y = −5
- Multiply equation 1 by 5 and equation 2 by 2 to match the x coefficients
- 10x − 20y = 120 and 10x + 10y = −30
- Subtract: −30y = 150, so y = −5
- Substitute back: x = 2
5.Solve simultaneously: 3x + 4y = 56 and 4x + 3y = 56
Answer: x = 8, y = 8
- Multiply equation 1 by 4 and equation 2 by 3 to match the x coefficients
- 12x + 16y = 224 and 12x + 9y = 168
- Subtract: 7y = 56, so y = 8
- Substitute back: x = 8
6.Solve simultaneously: 2x + 2y = 8 and 4x − 2y = −20
Answer: x = −2, y = 6
- Multiply equation 1 by 4 and equation 2 by 2 to match the x coefficients
- 8x + 8y = 32 and 8x − 4y = −40
- Subtract: 12y = 72, so y = 6
- Substitute back: x = −2
7.Solve simultaneously: 2x + y = −11 and 5x − 4y = −8
Answer: x = −4, y = −3
- Multiply equation 1 by 5 and equation 2 by 2 to match the x coefficients
- 10x + 5y = −55 and 10x − 8y = −16
- Subtract: 13y = −39, so y = −3
- Substitute back: x = −4
8.Solve simultaneously: 2x + 4y = 18 and 4x − 3y = 25
Answer: x = 7, y = 1
- Multiply equation 1 by 4 and equation 2 by 2 to match the x coefficients
- 8x + 16y = 72 and 8x − 6y = 50
- Subtract: 22y = 22, so y = 1
- Substitute back: x = 7
Marking tips
- Give credit for correct method even when the final answer slips — the working shows where the thinking went right.
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