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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 = 13 and x − y = 3. Find the value of x.
2. Solve the simultaneous equations x + y = 42 and x − y = 8. Find the value of x.
3. Solve the simultaneous equations x + y = 15 and x − y = 13. Find the value of x.
4. Solve the simultaneous equations x + y = 22 and x − y = 14. Find the value of x.
5. Solve the simultaneous equations x + y = 15 and x − y = 1. Find the value of x.
6. Solve the simultaneous equations x + y = 31 and x − y = 3. Find the value of x.
7. Solve the simultaneous equations x + y = 31 and x − y = 13. Find the value of x.
8. Solve the simultaneous equations x + y = 32 and x − y = 16. Find the value of x.
9. Solve the simultaneous equations x + y = 17 and x − y = 3. Find the value of x.
10. Solve the simultaneous equations x + y = 49 and x − y = 1. Find the value of x.
11. Solve the simultaneous equations x + y = 22 and x − y = 6. Find the value of x.
12. Solve the simultaneous equations x + y = 12 and x − y = 4. Find the value of x.
12 questions · Seed 45 · 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 = 13 and x − y = 3. Find the value of x.
8Add the two equations: 2x = 13 + 3 = 16, so x = 8 (and y = 5).
2. Solve the simultaneous equations x + y = 42 and x − y = 8. Find the value of x.
25Add the two equations: 2x = 42 + 8 = 50, so x = 25 (and y = 17).
3. Solve the simultaneous equations x + y = 15 and x − y = 13. Find the value of x.
14Add the two equations: 2x = 15 + 13 = 28, so x = 14 (and y = 1).
4. Solve the simultaneous equations x + y = 22 and x − y = 14. Find the value of x.
18Add the two equations: 2x = 22 + 14 = 36, so x = 18 (and y = 4).
5. Solve the simultaneous equations x + y = 15 and x − y = 1. Find the value of x.
8Add the two equations: 2x = 15 + 1 = 16, so x = 8 (and y = 7).
6. Solve the simultaneous equations x + y = 31 and x − y = 3. Find the value of x.
17Add the two equations: 2x = 31 + 3 = 34, so x = 17 (and y = 14).
7. Solve the simultaneous equations x + y = 31 and x − y = 13. Find the value of x.
22Add the two equations: 2x = 31 + 13 = 44, so x = 22 (and y = 9).
8. Solve the simultaneous equations x + y = 32 and x − y = 16. Find the value of x.
24Add the two equations: 2x = 32 + 16 = 48, so x = 24 (and y = 8).
9. Solve the simultaneous equations x + y = 17 and x − y = 3. Find the value of x.
10Add the two equations: 2x = 17 + 3 = 20, so x = 10 (and y = 7).
10. Solve the simultaneous equations x + y = 49 and x − y = 1. Find the value of x.
25Add the two equations: 2x = 49 + 1 = 50, so x = 25 (and y = 24).
11. Solve the simultaneous equations x + y = 22 and x − y = 6. Find the value of x.
14Add the two equations: 2x = 22 + 6 = 28, so x = 14 (and y = 8).
12. 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).
12 questions · Seed 45 · 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 = 13 and x − y = 3. Find the value of x.
2. Solve the simultaneous equations x + y = 42 and x − y = 8. Find the value of x.
3. Solve the simultaneous equations x + y = 15 and x − y = 13. Find the value of x.
4. Solve the simultaneous equations x + y = 22 and x − y = 14. Find the value of x.
5. Solve the simultaneous equations x + y = 15 and x − y = 1. Find the value of x.
6. Solve the simultaneous equations x + y = 31 and x − y = 3. Find the value of x.
7. Solve the simultaneous equations x + y = 31 and x − y = 13. Find the value of x.
8. Solve the simultaneous equations x + y = 32 and x − y = 16. Find the value of x.
9. Solve the simultaneous equations x + y = 17 and x − y = 3. Find the value of x.
10. Solve the simultaneous equations x + y = 49 and x − y = 1. Find the value of x.
11. Solve the simultaneous equations x + y = 22 and x − y = 6. Find the value of x.
12. Solve the simultaneous equations x + y = 12 and x − y = 4. Find the value of x.
12 questions · Seed 45 · 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 = 13 and x − y = 3. Find the value of x.
8Add the two equations: 2x = 13 + 3 = 16, so x = 8 (and y = 5).
2. Solve the simultaneous equations x + y = 42 and x − y = 8. Find the value of x.
25Add the two equations: 2x = 42 + 8 = 50, so x = 25 (and y = 17).
3. Solve the simultaneous equations x + y = 15 and x − y = 13. Find the value of x.
14Add the two equations: 2x = 15 + 13 = 28, so x = 14 (and y = 1).
4. Solve the simultaneous equations x + y = 22 and x − y = 14. Find the value of x.
18Add the two equations: 2x = 22 + 14 = 36, so x = 18 (and y = 4).
5. Solve the simultaneous equations x + y = 15 and x − y = 1. Find the value of x.
8Add the two equations: 2x = 15 + 1 = 16, so x = 8 (and y = 7).
6. Solve the simultaneous equations x + y = 31 and x − y = 3. Find the value of x.
17Add the two equations: 2x = 31 + 3 = 34, so x = 17 (and y = 14).
7. Solve the simultaneous equations x + y = 31 and x − y = 13. Find the value of x.
22Add the two equations: 2x = 31 + 13 = 44, so x = 22 (and y = 9).
8. Solve the simultaneous equations x + y = 32 and x − y = 16. Find the value of x.
24Add the two equations: 2x = 32 + 16 = 48, so x = 24 (and y = 8).
9. Solve the simultaneous equations x + y = 17 and x − y = 3. Find the value of x.
10Add the two equations: 2x = 17 + 3 = 20, so x = 10 (and y = 7).
10. Solve the simultaneous equations x + y = 49 and x − y = 1. Find the value of x.
25Add the two equations: 2x = 49 + 1 = 50, so x = 25 (and y = 24).
11. Solve the simultaneous equations x + y = 22 and x − y = 6. Find the value of x.
14Add the two equations: 2x = 22 + 6 = 28, so x = 14 (and y = 8).
12. 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).
12 questions · Seed 45 · Age guidance, not curriculum certification