Year 10 Simultaneous Equations Worksheet — Level 3 — Answers
Answer sheet with worked solutions for the Year 10 simultaneous equations worksheet.
Year 10 · Mathematics · Simultaneous Equations
Year 10 Simultaneous Equations Worksheet — Level 3 — Answers
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Solve each pair of equations. Check your solution satisfies both equations.
1.Solve simultaneously: 3x + 3y = 6 and 2x − 5y = −17
Answer: x = −1, y = 3
- Multiply equation 1 by 2 and equation 2 by 3 to match the x coefficients
- 6x + 6y = 12 and 6x − 15y = −51
- Subtract: 21y = 63, so y = 3
- Substitute back: x = −1
2.Solve simultaneously: 4x + 2y = 28 and 2x + 2y = 18
Answer: x = 5, y = 4
- Multiply equation 1 by 2 and equation 2 by 4 to match the x coefficients
- 8x + 4y = 56 and 8x + 8y = 72
- Subtract: −4y = −16, so y = 4
- Substitute back: x = 5
3.Solve simultaneously: 3x − y = −3 and 3x + 3y = −15
Answer: x = −2, y = −3
- Subtract equation 2 from equation 1: −4y = 12
- y = −3
- Substitute into equation 1: 3x + 3 = −3, so x = −2
4.Solve simultaneously: 3x − 4y = −6 and 4x − 5y = −6
Answer: x = 6, y = 6
- Multiply equation 1 by 4 and equation 2 by 3 to match the x coefficients
- 12x − 16y = −24 and 12x − 15y = −18
- Subtract: −y = −6, so y = 6
- Substitute back: x = 6
5.Solve simultaneously: 2x + 3y = 27 and 2x − 3y = −3
Answer: x = 6, y = 5
- Subtract equation 2 from equation 1: 6y = 30
- y = 5
- Substitute into equation 1: 2x + 15 = 27, so x = 6
6.Solve simultaneously: 3x − 3y = −39 and 3x + 2y = −4
Answer: x = −6, y = 7
- Subtract equation 2 from equation 1: −5y = −35
- y = 7
- Substitute into equation 1: 3x − 21 = −39, so x = −6
7.Solve simultaneously: 3x + y = 21 and 4x − 5y = 47
Answer: x = 8, y = −3
- Multiply equation 1 by 4 and equation 2 by 3 to match the x coefficients
- 12x + 4y = 84 and 12x − 15y = 141
- Subtract: 19y = −57, so y = −3
- Substitute back: x = 8
8.Solve simultaneously: 2x − y = 1 and 2x + 4y = 36
Answer: x = 4, y = 7
- Subtract equation 2 from equation 1: −5y = −35
- y = 7
- Substitute into equation 1: 2x − 7 = 1, so x = 4
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