Success TutoringWorksheets

11th Grade Systems of Equations Worksheet — Level 3 — Practice Set 4 — Answers

Answer sheet with worked solutions for the 11th Grade systems of equations worksheet.

Download answers PDFPrint answersBack to worksheet
Success TutoringWorksheetsAnswer sheet11th Grade · Mathematics · Simultaneous Equations

11th Grade Systems of Equations Worksheet — Level 3 — Practice Set 4 — Answers

Solve each pair of equations. Check your solution satisfies both equations.

1.Solve the system: 3x − 3y = 3 and 3x − 2y = 5

Answer: x = 3, y = 2

  1. Subtract equation 2 from equation 1: −y = −2
  2. y = 2
  3. Substitute into equation 1: 3x − 6 = 3, so x = 3
2.Solve the system: 4x − y = 8 and 3x − 5y = −11

Answer: x = 3, y = 4

  1. Multiply equation 1 by 3 and equation 2 by 4 to match the x coefficients
  2. 12x − 3y = 24 and 12x − 20y = −44
  3. Subtract: 17y = 68, so y = 4
  4. Substitute back: x = 3
3.Solve the system: 2x − y = 12 and 4x − 3y = 26

Answer: x = 5, y = −2

  1. Multiply equation 1 by 4 and equation 2 by 2 to match the x coefficients
  2. 8x − 4y = 48 and 8x − 6y = 52
  3. Subtract: 2y = −4, so y = −2
  4. Substitute back: x = 5
4.Solve the system: 4x + 4y = −4 and 2x − 2y = −10

Answer: x = −3, y = 2

  1. Multiply equation 1 by 2 and equation 2 by 4 to match the x coefficients
  2. 8x + 8y = −8 and 8x − 8y = −40
  3. Subtract: 16y = 32, so y = 2
  4. Substitute back: x = −3
5.Solve the system: 2x − 3y = 27 and 2x + 5y = −13

Answer: x = 6, y = −5

  1. Subtract equation 2 from equation 1: −8y = 40
  2. y = −5
  3. Substitute into equation 1: 2x + 15 = 27, so x = 6
6.Solve the system: 3x + 3y = 12 and 2x + y = 9

Answer: x = 5, y = −1

  1. Multiply equation 1 by 2 and equation 2 by 3 to match the x coefficients
  2. 6x + 6y = 24 and 6x + 3y = 27
  3. Subtract: 3y = −3, so y = −1
  4. Substitute back: x = 5
7.Solve the system: 2x + y = 13 and 4x + 3y = 29

Answer: x = 5, y = 3

  1. Multiply equation 1 by 4 and equation 2 by 2 to match the x coefficients
  2. 8x + 4y = 52 and 8x + 6y = 58
  3. Subtract: −2y = −6, so y = 3
  4. Substitute back: x = 5
8.Solve the system: 4x + 2y = 40 and 5x + y = 38

Answer: x = 6, y = 8

  1. Multiply equation 1 by 5 and equation 2 by 4 to match the x coefficients
  2. 20x + 10y = 200 and 20x + 4y = 152
  3. Subtract: 6y = 48, so y = 8
  4. Substitute back: x = 6
Free worksheets at worksheets.successtutoring.com · © Success Tutoring · Free for personal and classroom use

Marking tips

  • Give credit for correct method even when the final answer slips — the working shows where the thinking went right.
  • For open-ended tasks, use the success criteria as a checklist rather than looking for one "right" answer.
  • Celebrate what went well first, then pick one thing to work on next.

Great work. Here's what to try next: