Year 9 Simultaneous Equations Worksheet — Level 3 — Practice Set 4 — 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 — Practice Set 4 — Answers
Solve each pair of equations. Check your solution satisfies both equations.
1.Solve simultaneously: 4x − 3y = 7 and 3x + 2y = 1
Answer: x = 1, y = −1
- Multiply equation 1 by 3 and equation 2 by 4 to match the x coefficients
- 12x − 9y = 21 and 12x + 8y = 4
- Subtract: −17y = 17, so y = −1
- Substitute back: x = 1
2.Solve simultaneously: 3x − y = 17 and 4x − 4y = 36
Answer: x = 4, y = −5
- Multiply equation 1 by 4 and equation 2 by 3 to match the x coefficients
- 12x − 4y = 68 and 12x − 12y = 108
- Subtract: 8y = −40, so y = −5
- Substitute back: x = 4
3.Solve simultaneously: 4x − y = −27 and 5x + 5y = 10
Answer: x = −5, y = 7
- Multiply equation 1 by 5 and equation 2 by 4 to match the x coefficients
- 20x − 5y = −135 and 20x + 20y = 40
- Subtract: −25y = −175, so y = 7
- Substitute back: x = −5
4.Solve simultaneously: 3x − y = −10 and 3x + y = −14
Answer: x = −4, y = −2
- Subtract equation 2 from equation 1: −2y = 4
- y = −2
- Substitute into equation 1: 3x + 2 = −10, so x = −4
5.Solve simultaneously: 3x − y = −11 and 3x + 5y = −35
Answer: x = −5, y = −4
- Subtract equation 2 from equation 1: −6y = 24
- y = −4
- Substitute into equation 1: 3x + 4 = −11, so x = −5
6.Solve simultaneously: 4x − y = −24 and 5x + 5y = 20
Answer: x = −4, y = 8
- Multiply equation 1 by 5 and equation 2 by 4 to match the x coefficients
- 20x − 5y = −120 and 20x + 20y = 80
- Subtract: −25y = −200, so y = 8
- Substitute back: x = −4
7.Solve simultaneously: 4x − 2y = −8 and 5x − 2y = −13
Answer: x = −5, y = −6
- Multiply equation 1 by 5 and equation 2 by 4 to match the x coefficients
- 20x − 10y = −40 and 20x − 8y = −52
- Subtract: −2y = 12, so y = −6
- Substitute back: x = −5
8.Solve simultaneously: 4x − 2y = 32 and 2x + y = 8
Answer: x = 6, y = −4
- Multiply equation 1 by 2 and equation 2 by 4 to match the x coefficients
- 8x − 4y = 64 and 8x + 4y = 32
- Subtract: −8y = 32, so y = −4
- Substitute back: x = 6
Marking tips
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