Back to worksheetsMathsAges 16-18
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 16-18
Simultaneous linear equations
Take your time. Show your thinking.
1. Solve the simultaneous equations x + y = 21 and x − y = 19. Find the value of x.
2. Solve the simultaneous equations x + y = 11 and x − y = 1. Find the value of x.
3. Solve the simultaneous equations x + y = 31 and x − y = 7. Find the value of x.
4. Solve the simultaneous equations x + y = 18 and x − y = 2. Find the value of x.
5. Solve the simultaneous equations x + y = 12 and x − y = 4. Find the value of x.
6. Solve the simultaneous equations x + y = 37 and x − y = 11. Find the value of x.
7. Solve the simultaneous equations x + y = 31 and x − y = 17. Find the value of x.
8. Solve the simultaneous equations x + y = 17 and x − y = 15. Find the value of x.
9. Solve the simultaneous equations x + y = 35 and x − y = 15. Find the value of x.
10. Solve the simultaneous equations x + y = 33 and x − y = 7. Find the value of x.
11. Solve the simultaneous equations x + y = 29 and x − y = 9. Find the value of x.
12. Solve the simultaneous equations x + y = 34 and x − y = 14. Find the value of x.
12 questions · Seed 104731 · Age guidance, not curriculum certification
View the answer key
Worksheet StudioAnswer key · Ages 16-18
Simultaneous linear equations
Answers and reasoning. Review before teaching.
1. Solve the simultaneous equations x + y = 21 and x − y = 19. Find the value of x.
20Add the two equations: 2x = 21 + 19 = 40, so x = 20 (and y = 1).
2. Solve the simultaneous equations x + y = 11 and x − y = 1. Find the value of x.
6Add the two equations: 2x = 11 + 1 = 12, so x = 6 (and y = 5).
3. Solve the simultaneous equations x + y = 31 and x − y = 7. Find the value of x.
19Add the two equations: 2x = 31 + 7 = 38, so x = 19 (and y = 12).
4. Solve the simultaneous equations x + y = 18 and x − y = 2. Find the value of x.
10Add the two equations: 2x = 18 + 2 = 20, so x = 10 (and y = 8).
5. Solve the simultaneous equations x + y = 12 and x − y = 4. Find the value of x.
8Add the two equations: 2x = 12 + 4 = 16, so x = 8 (and y = 4).
6. Solve the simultaneous equations x + y = 37 and x − y = 11. Find the value of x.
24Add the two equations: 2x = 37 + 11 = 48, so x = 24 (and y = 13).
7. Solve the simultaneous equations x + y = 31 and x − y = 17. Find the value of x.
24Add the two equations: 2x = 31 + 17 = 48, so x = 24 (and y = 7).
8. Solve the simultaneous equations x + y = 17 and x − y = 15. Find the value of x.
16Add the two equations: 2x = 17 + 15 = 32, so x = 16 (and y = 1).
9. Solve the simultaneous equations x + y = 35 and x − y = 15. Find the value of x.
25Add the two equations: 2x = 35 + 15 = 50, so x = 25 (and y = 10).
10. Solve the simultaneous equations x + y = 33 and x − y = 7. Find the value of x.
20Add the two equations: 2x = 33 + 7 = 40, so x = 20 (and y = 13).
11. Solve the simultaneous equations x + y = 29 and x − y = 9. Find the value of x.
19Add the two equations: 2x = 29 + 9 = 38, so x = 19 (and y = 10).
12. Solve the simultaneous equations x + y = 34 and x − y = 14. Find the value of x.
24Add the two equations: 2x = 34 + 14 = 48, so x = 24 (and y = 10).
12 questions · Seed 104731 · Age guidance, not curriculum certification
Worksheet StudioPractice pack · Ages 16-18
Simultaneous linear equations
Take your time. Show your thinking.
1. Solve the simultaneous equations x + y = 21 and x − y = 19. Find the value of x.
2. Solve the simultaneous equations x + y = 11 and x − y = 1. Find the value of x.
3. Solve the simultaneous equations x + y = 31 and x − y = 7. Find the value of x.
4. Solve the simultaneous equations x + y = 18 and x − y = 2. Find the value of x.
5. Solve the simultaneous equations x + y = 12 and x − y = 4. Find the value of x.
6. Solve the simultaneous equations x + y = 37 and x − y = 11. Find the value of x.
7. Solve the simultaneous equations x + y = 31 and x − y = 17. Find the value of x.
8. Solve the simultaneous equations x + y = 17 and x − y = 15. Find the value of x.
9. Solve the simultaneous equations x + y = 35 and x − y = 15. Find the value of x.
10. Solve the simultaneous equations x + y = 33 and x − y = 7. Find the value of x.
11. Solve the simultaneous equations x + y = 29 and x − y = 9. Find the value of x.
12. Solve the simultaneous equations x + y = 34 and x − y = 14. Find the value of x.
12 questions · Seed 104731 · Age guidance, not curriculum certification
Worksheet StudioAnswer key · Ages 16-18
Simultaneous linear equations
Answers and reasoning. Review before teaching.
1. Solve the simultaneous equations x + y = 21 and x − y = 19. Find the value of x.
20Add the two equations: 2x = 21 + 19 = 40, so x = 20 (and y = 1).
2. Solve the simultaneous equations x + y = 11 and x − y = 1. Find the value of x.
6Add the two equations: 2x = 11 + 1 = 12, so x = 6 (and y = 5).
3. Solve the simultaneous equations x + y = 31 and x − y = 7. Find the value of x.
19Add the two equations: 2x = 31 + 7 = 38, so x = 19 (and y = 12).
4. Solve the simultaneous equations x + y = 18 and x − y = 2. Find the value of x.
10Add the two equations: 2x = 18 + 2 = 20, so x = 10 (and y = 8).
5. Solve the simultaneous equations x + y = 12 and x − y = 4. Find the value of x.
8Add the two equations: 2x = 12 + 4 = 16, so x = 8 (and y = 4).
6. Solve the simultaneous equations x + y = 37 and x − y = 11. Find the value of x.
24Add the two equations: 2x = 37 + 11 = 48, so x = 24 (and y = 13).
7. Solve the simultaneous equations x + y = 31 and x − y = 17. Find the value of x.
24Add the two equations: 2x = 31 + 17 = 48, so x = 24 (and y = 7).
8. Solve the simultaneous equations x + y = 17 and x − y = 15. Find the value of x.
16Add the two equations: 2x = 17 + 15 = 32, so x = 16 (and y = 1).
9. Solve the simultaneous equations x + y = 35 and x − y = 15. Find the value of x.
25Add the two equations: 2x = 35 + 15 = 50, so x = 25 (and y = 10).
10. Solve the simultaneous equations x + y = 33 and x − y = 7. Find the value of x.
20Add the two equations: 2x = 33 + 7 = 40, so x = 20 (and y = 13).
11. Solve the simultaneous equations x + y = 29 and x − y = 9. Find the value of x.
19Add the two equations: 2x = 29 + 9 = 38, so x = 19 (and y = 10).
12. Solve the simultaneous equations x + y = 34 and x − y = 14. Find the value of x.
24Add the two equations: 2x = 34 + 14 = 48, so x = 24 (and y = 10).
12 questions · Seed 104731 · Age guidance, not curriculum certification