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 = 18 and x − y = 8. Find the value of x.
2. Solve the simultaneous equations x + y = 23 and x − y = 1. Find the value of x.
3. Solve the simultaneous equations x + y = 25 and x − y = 3. Find the value of x.
4. Solve the simultaneous equations x + y = 32 and x − y = 10. Find the value of x.
5. Solve the simultaneous equations x + y = 46 and x − y = 4. Find the value of x.
6. Solve the simultaneous equations x + y = 11 and x − y = 5. Find the value of x.
7. Solve the simultaneous equations x + y = 36 and x − y = 12. Find the value of x.
8. Solve the simultaneous equations x + y = 26 and x − y = 4. Find the value of x.
9. Solve the simultaneous equations x + y = 38 and x − y = 2. Find the value of x.
10. Solve the simultaneous equations x + y = 19 and x − y = 5. Find the value of x.
11. Solve the simultaneous equations x + y = 20 and x − y = 6. Find the value of x.
12. Solve the simultaneous equations x + y = 16 and x − y = 14. Find the value of x.
12 questions · Seed 104739 · 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 = 18 and x − y = 8. Find the value of x.
13Add the two equations: 2x = 18 + 8 = 26, so x = 13 (and y = 5).
2. Solve the simultaneous equations x + y = 23 and x − y = 1. Find the value of x.
12Add the two equations: 2x = 23 + 1 = 24, so x = 12 (and y = 11).
3. Solve the simultaneous equations x + y = 25 and x − y = 3. Find the value of x.
14Add the two equations: 2x = 25 + 3 = 28, so x = 14 (and y = 11).
4. Solve the simultaneous equations x + y = 32 and x − y = 10. Find the value of x.
21Add the two equations: 2x = 32 + 10 = 42, so x = 21 (and y = 11).
5. Solve the simultaneous equations x + y = 46 and x − y = 4. Find the value of x.
25Add the two equations: 2x = 46 + 4 = 50, so x = 25 (and y = 21).
6. Solve the simultaneous equations x + y = 11 and x − y = 5. Find the value of x.
8Add the two equations: 2x = 11 + 5 = 16, so x = 8 (and y = 3).
7. Solve the simultaneous equations x + y = 36 and x − y = 12. Find the value of x.
24Add the two equations: 2x = 36 + 12 = 48, so x = 24 (and y = 12).
8. Solve the simultaneous equations x + y = 26 and x − y = 4. Find the value of x.
15Add the two equations: 2x = 26 + 4 = 30, so x = 15 (and y = 11).
9. Solve the simultaneous equations x + y = 38 and x − y = 2. Find the value of x.
20Add the two equations: 2x = 38 + 2 = 40, so x = 20 (and y = 18).
10. Solve the simultaneous equations x + y = 19 and x − y = 5. Find the value of x.
12Add the two equations: 2x = 19 + 5 = 24, so x = 12 (and y = 7).
11. Solve the simultaneous equations x + y = 20 and x − y = 6. Find the value of x.
13Add the two equations: 2x = 20 + 6 = 26, so x = 13 (and y = 7).
12. Solve the simultaneous equations x + y = 16 and x − y = 14. Find the value of x.
15Add the two equations: 2x = 16 + 14 = 30, so x = 15 (and y = 1).
12 questions · Seed 104739 · 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 = 18 and x − y = 8. Find the value of x.
2. Solve the simultaneous equations x + y = 23 and x − y = 1. Find the value of x.
3. Solve the simultaneous equations x + y = 25 and x − y = 3. Find the value of x.
4. Solve the simultaneous equations x + y = 32 and x − y = 10. Find the value of x.
5. Solve the simultaneous equations x + y = 46 and x − y = 4. Find the value of x.
6. Solve the simultaneous equations x + y = 11 and x − y = 5. Find the value of x.
7. Solve the simultaneous equations x + y = 36 and x − y = 12. Find the value of x.
8. Solve the simultaneous equations x + y = 26 and x − y = 4. Find the value of x.
9. Solve the simultaneous equations x + y = 38 and x − y = 2. Find the value of x.
10. Solve the simultaneous equations x + y = 19 and x − y = 5. Find the value of x.
11. Solve the simultaneous equations x + y = 20 and x − y = 6. Find the value of x.
12. Solve the simultaneous equations x + y = 16 and x − y = 14. Find the value of x.
12 questions · Seed 104739 · 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 = 18 and x − y = 8. Find the value of x.
13Add the two equations: 2x = 18 + 8 = 26, so x = 13 (and y = 5).
2. Solve the simultaneous equations x + y = 23 and x − y = 1. Find the value of x.
12Add the two equations: 2x = 23 + 1 = 24, so x = 12 (and y = 11).
3. Solve the simultaneous equations x + y = 25 and x − y = 3. Find the value of x.
14Add the two equations: 2x = 25 + 3 = 28, so x = 14 (and y = 11).
4. Solve the simultaneous equations x + y = 32 and x − y = 10. Find the value of x.
21Add the two equations: 2x = 32 + 10 = 42, so x = 21 (and y = 11).
5. Solve the simultaneous equations x + y = 46 and x − y = 4. Find the value of x.
25Add the two equations: 2x = 46 + 4 = 50, so x = 25 (and y = 21).
6. Solve the simultaneous equations x + y = 11 and x − y = 5. Find the value of x.
8Add the two equations: 2x = 11 + 5 = 16, so x = 8 (and y = 3).
7. Solve the simultaneous equations x + y = 36 and x − y = 12. Find the value of x.
24Add the two equations: 2x = 36 + 12 = 48, so x = 24 (and y = 12).
8. Solve the simultaneous equations x + y = 26 and x − y = 4. Find the value of x.
15Add the two equations: 2x = 26 + 4 = 30, so x = 15 (and y = 11).
9. Solve the simultaneous equations x + y = 38 and x − y = 2. Find the value of x.
20Add the two equations: 2x = 38 + 2 = 40, so x = 20 (and y = 18).
10. Solve the simultaneous equations x + y = 19 and x − y = 5. Find the value of x.
12Add the two equations: 2x = 19 + 5 = 24, so x = 12 (and y = 7).
11. Solve the simultaneous equations x + y = 20 and x − y = 6. Find the value of x.
13Add the two equations: 2x = 20 + 6 = 26, so x = 13 (and y = 7).
12. Solve the simultaneous equations x + y = 16 and x − y = 14. Find the value of x.
15Add the two equations: 2x = 16 + 14 = 30, so x = 15 (and y = 1).
12 questions · Seed 104739 · Age guidance, not curriculum certification