Back to worksheetsMathsAges 13-15
Simultaneous linear equations
Eliminate y by adding x + y and x − y to solve a pair of simultaneous linear equations. Review suitability for your learners before teaching.
Worksheet StudioPractice pack · Ages 13-15
Simultaneous linear equations
Take your time. Show your thinking.
1. Solve the simultaneous equations x + y = 7 and x − y = 3. Find the value of x.
2. Solve the simultaneous equations x + y = 17 and x − y = 13. Find the value of x.
3. Solve the simultaneous equations x + y = 22 and x − y = 20. Find the value of x.
4. Solve the simultaneous equations x + y = 29 and x − y = 13. Find the value of x.
5. Solve the simultaneous equations x + y = 29 and x − y = 15. Find the value of x.
6. Solve the simultaneous equations x + y = 35 and x − y = 5. Find the value of x.
7. Solve the simultaneous equations x + y = 19 and x − y = 7. Find the value of x.
8. Solve the simultaneous equations x + y = 21 and x − y = 1. Find the value of x.
9. Solve the simultaneous equations x + y = 21 and x − y = 7. Find the value of x.
10. Solve the simultaneous equations x + y = 30 and x − y = 2. Find the value of x.
11. Solve the simultaneous equations x + y = 10 and x − y = 2. Find the value of x.
12. Solve the simultaneous equations x + y = 29 and x − y = 17. Find the value of x.
12 questions · Seed 104729 · Age guidance, not curriculum certification
View the answer key
Worksheet StudioAnswer key · Ages 13-15
Simultaneous linear equations
Answers and reasoning. Review before teaching.
1. Solve the simultaneous equations x + y = 7 and x − y = 3. Find the value of x.
5Add the two equations: 2x = 7 + 3 = 10, so x = 5 (and y = 2).
2. Solve the simultaneous equations x + y = 17 and x − y = 13. Find the value of x.
15Add the two equations: 2x = 17 + 13 = 30, so x = 15 (and y = 2).
3. Solve the simultaneous equations x + y = 22 and x − y = 20. Find the value of x.
21Add the two equations: 2x = 22 + 20 = 42, so x = 21 (and y = 1).
4. Solve the simultaneous equations x + y = 29 and x − y = 13. Find the value of x.
21Add the two equations: 2x = 29 + 13 = 42, so x = 21 (and y = 8).
5. Solve the simultaneous equations x + y = 29 and x − y = 15. Find the value of x.
22Add the two equations: 2x = 29 + 15 = 44, so x = 22 (and y = 7).
6. Solve the simultaneous equations x + y = 35 and x − y = 5. Find the value of x.
20Add the two equations: 2x = 35 + 5 = 40, so x = 20 (and y = 15).
7. Solve the simultaneous equations x + y = 19 and x − y = 7. Find the value of x.
13Add the two equations: 2x = 19 + 7 = 26, so x = 13 (and y = 6).
8. Solve the simultaneous equations x + y = 21 and x − y = 1. Find the value of x.
11Add the two equations: 2x = 21 + 1 = 22, so x = 11 (and y = 10).
9. Solve the simultaneous equations x + y = 21 and x − y = 7. Find the value of x.
14Add the two equations: 2x = 21 + 7 = 28, so x = 14 (and y = 7).
10. Solve the simultaneous equations x + y = 30 and x − y = 2. Find the value of x.
16Add the two equations: 2x = 30 + 2 = 32, so x = 16 (and y = 14).
11. Solve the simultaneous equations x + y = 10 and x − y = 2. Find the value of x.
6Add the two equations: 2x = 10 + 2 = 12, so x = 6 (and y = 4).
12. Solve the simultaneous equations x + y = 29 and x − y = 17. Find the value of x.
23Add the two equations: 2x = 29 + 17 = 46, so x = 23 (and y = 6).
12 questions · Seed 104729 · Age guidance, not curriculum certification
Worksheet StudioPractice pack · Ages 13-15
Simultaneous linear equations
Take your time. Show your thinking.
1. Solve the simultaneous equations x + y = 7 and x − y = 3. Find the value of x.
2. Solve the simultaneous equations x + y = 17 and x − y = 13. Find the value of x.
3. Solve the simultaneous equations x + y = 22 and x − y = 20. Find the value of x.
4. Solve the simultaneous equations x + y = 29 and x − y = 13. Find the value of x.
5. Solve the simultaneous equations x + y = 29 and x − y = 15. Find the value of x.
6. Solve the simultaneous equations x + y = 35 and x − y = 5. Find the value of x.
7. Solve the simultaneous equations x + y = 19 and x − y = 7. Find the value of x.
8. Solve the simultaneous equations x + y = 21 and x − y = 1. Find the value of x.
9. Solve the simultaneous equations x + y = 21 and x − y = 7. Find the value of x.
10. Solve the simultaneous equations x + y = 30 and x − y = 2. Find the value of x.
11. Solve the simultaneous equations x + y = 10 and x − y = 2. Find the value of x.
12. Solve the simultaneous equations x + y = 29 and x − y = 17. Find the value of x.
12 questions · Seed 104729 · Age guidance, not curriculum certification
Worksheet StudioAnswer key · Ages 13-15
Simultaneous linear equations
Answers and reasoning. Review before teaching.
1. Solve the simultaneous equations x + y = 7 and x − y = 3. Find the value of x.
5Add the two equations: 2x = 7 + 3 = 10, so x = 5 (and y = 2).
2. Solve the simultaneous equations x + y = 17 and x − y = 13. Find the value of x.
15Add the two equations: 2x = 17 + 13 = 30, so x = 15 (and y = 2).
3. Solve the simultaneous equations x + y = 22 and x − y = 20. Find the value of x.
21Add the two equations: 2x = 22 + 20 = 42, so x = 21 (and y = 1).
4. Solve the simultaneous equations x + y = 29 and x − y = 13. Find the value of x.
21Add the two equations: 2x = 29 + 13 = 42, so x = 21 (and y = 8).
5. Solve the simultaneous equations x + y = 29 and x − y = 15. Find the value of x.
22Add the two equations: 2x = 29 + 15 = 44, so x = 22 (and y = 7).
6. Solve the simultaneous equations x + y = 35 and x − y = 5. Find the value of x.
20Add the two equations: 2x = 35 + 5 = 40, so x = 20 (and y = 15).
7. Solve the simultaneous equations x + y = 19 and x − y = 7. Find the value of x.
13Add the two equations: 2x = 19 + 7 = 26, so x = 13 (and y = 6).
8. Solve the simultaneous equations x + y = 21 and x − y = 1. Find the value of x.
11Add the two equations: 2x = 21 + 1 = 22, so x = 11 (and y = 10).
9. Solve the simultaneous equations x + y = 21 and x − y = 7. Find the value of x.
14Add the two equations: 2x = 21 + 7 = 28, so x = 14 (and y = 7).
10. Solve the simultaneous equations x + y = 30 and x − y = 2. Find the value of x.
16Add the two equations: 2x = 30 + 2 = 32, so x = 16 (and y = 14).
11. Solve the simultaneous equations x + y = 10 and x − y = 2. Find the value of x.
6Add the two equations: 2x = 10 + 2 = 12, so x = 6 (and y = 4).
12. Solve the simultaneous equations x + y = 29 and x − y = 17. Find the value of x.
23Add the two equations: 2x = 29 + 17 = 46, so x = 23 (and y = 6).
12 questions · Seed 104729 · Age guidance, not curriculum certification