Year 9 Simultaneous Equations Worksheet — Level 3 — Answers
Answer sheet with worked solutions for the Year 9 simultaneous equations worksheet.
Success TutoringWorksheetsAnswer sheetYear 9 · Mathematics · Simultaneous EquationsYear 9 Simultaneous Equations Worksheet — Level 3 — Answers
Solve each pair of equations. Check your solution satisfies both equations.
1.Solve simultaneously: 2x − 3y = −11 and 4x − 4y = −12
Answer: x = 2, y = 5
- Multiply equation 1 by 4 and equation 2 by 2 to match the x coefficients
- 8x − 12y = −44 and 8x − 8y = −24
- Subtract: −4y = −20, so y = 5
- Substitute back: x = 2
2.Solve simultaneously: 3x + y = −11 and 2x + 3y = 9
Answer: x = −6, y = 7
- Multiply equation 1 by 2 and equation 2 by 3 to match the x coefficients
- 6x + 2y = −22 and 6x + 9y = 27
- Subtract: −7y = −49, so y = 7
- Substitute back: x = −6
3.Solve simultaneously: 2x + 2y = 16 and 3x + 4y = 26
Answer: x = 6, y = 2
- Multiply equation 1 by 3 and equation 2 by 2 to match the x coefficients
- 6x + 6y = 48 and 6x + 8y = 52
- Subtract: −2y = −4, so y = 2
- Substitute back: x = 6
4.Solve simultaneously: 2x + 4y = −4 and 5x − 4y = 46
Answer: x = 6, y = −4
- Multiply equation 1 by 5 and equation 2 by 2 to match the x coefficients
- 10x + 20y = −20 and 10x − 8y = 92
- Subtract: 28y = −112, so y = −4
- Substitute back: x = 6
5.Solve simultaneously: 3x − y = 22 and 4x + 3y = 38
Answer: x = 8, y = 2
- Multiply equation 1 by 4 and equation 2 by 3 to match the x coefficients
- 12x − 4y = 88 and 12x + 9y = 114
- Subtract: −13y = −26, so y = 2
- Substitute back: x = 8
6.Solve simultaneously: 3x − 4y = −26 and 2x − 2y = −16
Answer: x = −6, y = 2
- Multiply equation 1 by 2 and equation 2 by 3 to match the x coefficients
- 6x − 8y = −52 and 6x − 6y = −48
- Subtract: −2y = −4, so y = 2
- Substitute back: x = −6
7.Solve simultaneously: 2x + 3y = −4 and 2x + 2y = −6
Answer: x = −5, y = 2
- Subtract equation 2 from equation 1: y = 2
- y = 2
- Substitute into equation 1: 2x + 6 = −4, so x = −5
8.Solve simultaneously: 2x + y = −6 and 3x − 2y = 5
Answer: x = −1, y = −4
- Multiply equation 1 by 3 and equation 2 by 2 to match the x coefficients
- 6x + 3y = −18 and 6x − 4y = 10
- Subtract: 7y = −28, so y = −4
- Substitute back: x = −1
Marking tips
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