MathsAges 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.

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Age band:Ages 13-15 Ages 16-18

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Worksheet StudioPractice pack · Ages 13-15

Simultaneous linear equations

Take your time. Show your thinking.

1. Solve the simultaneous equations x + y = 30 and x − y = 16. Find the value of x.
30 · 16 · Simultaneous linear equati…
2. Solve the simultaneous equations x + y = 17 and x − y = 1. Find the value of x.
17 · 1 · Simultaneous linear equati…
3. Solve the simultaneous equations x + y = 19 and x − y = 15. Find the value of x.
19 · 15 · Simultaneous linear equati…
4. Solve the simultaneous equations x + y = 13 and x − y = 1. Find the value of x.
13 · 1 · Simultaneous linear equati…
5. Solve the simultaneous equations x + y = 18 and x − y = 8. Find the value of x.
18 · 8 · Simultaneous linear equati…
6. Solve the simultaneous equations x + y = 15 and x − y = 9. Find the value of x.
15 · 9 · Simultaneous linear equati…
7. Solve the simultaneous equations x + y = 41 and x − y = 9. Find the value of x.
41 · 9 · Simultaneous linear equati…
8. Solve the simultaneous equations x + y = 31 and x − y = 19. Find the value of x.
31 · 19 · Simultaneous linear equati…
9. Solve the simultaneous equations x + y = 16 and x − y = 14. Find the value of x.
16 · 14 · Simultaneous linear equati…
10. Solve the simultaneous equations x + y = 11 and x − y = 3. Find the value of x.
11 · 3 · Simultaneous linear equati…
11. Solve the simultaneous equations x + y = 26 and x − y = 16. Find the value of x.
26 · 16 · Simultaneous linear equati…
12. Solve the simultaneous equations x + y = 33 and x − y = 3. Find the value of x.
33 · 3 · Simultaneous linear equati…

12 questions · Seed 104737 · Age guidance, not curriculum certification

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Worksheet StudioAnswer key · Ages 13-15

Simultaneous linear equations

Answers and reasoning. Review before teaching.

1. Solve the simultaneous equations x + y = 30 and x − y = 16. Find the value of x.
23
Add the two equations: 2x = 30 + 16 = 46, so x = 23 (and y = 7).
2. Solve the simultaneous equations x + y = 17 and x − y = 1. Find the value of x.
9
Add the two equations: 2x = 17 + 1 = 18, so x = 9 (and y = 8).
3. Solve the simultaneous equations x + y = 19 and x − y = 15. Find the value of x.
17
Add the two equations: 2x = 19 + 15 = 34, so x = 17 (and y = 2).
4. Solve the simultaneous equations x + y = 13 and x − y = 1. Find the value of x.
7
Add the two equations: 2x = 13 + 1 = 14, so x = 7 (and y = 6).
5. Solve the simultaneous equations x + y = 18 and x − y = 8. Find the value of x.
13
Add the two equations: 2x = 18 + 8 = 26, so x = 13 (and y = 5).
6. Solve the simultaneous equations x + y = 15 and x − y = 9. Find the value of x.
12
Add the two equations: 2x = 15 + 9 = 24, so x = 12 (and y = 3).
7. Solve the simultaneous equations x + y = 41 and x − y = 9. Find the value of x.
25
Add the two equations: 2x = 41 + 9 = 50, so x = 25 (and y = 16).
8. Solve the simultaneous equations x + y = 31 and x − y = 19. Find the value of x.
25
Add the two equations: 2x = 31 + 19 = 50, so x = 25 (and y = 6).
9. Solve the simultaneous equations x + y = 16 and x − y = 14. Find the value of x.
15
Add the two equations: 2x = 16 + 14 = 30, so x = 15 (and y = 1).
10. Solve the simultaneous equations x + y = 11 and x − y = 3. Find the value of x.
7
Add the two equations: 2x = 11 + 3 = 14, so x = 7 (and y = 4).
11. Solve the simultaneous equations x + y = 26 and x − y = 16. Find the value of x.
21
Add the two equations: 2x = 26 + 16 = 42, so x = 21 (and y = 5).
12. Solve the simultaneous equations x + y = 33 and x − y = 3. Find the value of x.
18
Add the two equations: 2x = 33 + 3 = 36, so x = 18 (and y = 15).

12 questions · Seed 104737 · 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 = 30 and x − y = 16. Find the value of x.
30 · 16 · Simultaneous linear equati…
2. Solve the simultaneous equations x + y = 17 and x − y = 1. Find the value of x.
17 · 1 · Simultaneous linear equati…
3. Solve the simultaneous equations x + y = 19 and x − y = 15. Find the value of x.
19 · 15 · Simultaneous linear equati…
4. Solve the simultaneous equations x + y = 13 and x − y = 1. Find the value of x.
13 · 1 · Simultaneous linear equati…
5. Solve the simultaneous equations x + y = 18 and x − y = 8. Find the value of x.
18 · 8 · Simultaneous linear equati…
6. Solve the simultaneous equations x + y = 15 and x − y = 9. Find the value of x.
15 · 9 · Simultaneous linear equati…
7. Solve the simultaneous equations x + y = 41 and x − y = 9. Find the value of x.
41 · 9 · Simultaneous linear equati…
8. Solve the simultaneous equations x + y = 31 and x − y = 19. Find the value of x.
31 · 19 · Simultaneous linear equati…
9. Solve the simultaneous equations x + y = 16 and x − y = 14. Find the value of x.
16 · 14 · Simultaneous linear equati…
10. Solve the simultaneous equations x + y = 11 and x − y = 3. Find the value of x.
11 · 3 · Simultaneous linear equati…
11. Solve the simultaneous equations x + y = 26 and x − y = 16. Find the value of x.
26 · 16 · Simultaneous linear equati…
12. Solve the simultaneous equations x + y = 33 and x − y = 3. Find the value of x.
33 · 3 · Simultaneous linear equati…

12 questions · Seed 104737 · 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 = 30 and x − y = 16. Find the value of x.
23
Add the two equations: 2x = 30 + 16 = 46, so x = 23 (and y = 7).
2. Solve the simultaneous equations x + y = 17 and x − y = 1. Find the value of x.
9
Add the two equations: 2x = 17 + 1 = 18, so x = 9 (and y = 8).
3. Solve the simultaneous equations x + y = 19 and x − y = 15. Find the value of x.
17
Add the two equations: 2x = 19 + 15 = 34, so x = 17 (and y = 2).
4. Solve the simultaneous equations x + y = 13 and x − y = 1. Find the value of x.
7
Add the two equations: 2x = 13 + 1 = 14, so x = 7 (and y = 6).
5. Solve the simultaneous equations x + y = 18 and x − y = 8. Find the value of x.
13
Add the two equations: 2x = 18 + 8 = 26, so x = 13 (and y = 5).
6. Solve the simultaneous equations x + y = 15 and x − y = 9. Find the value of x.
12
Add the two equations: 2x = 15 + 9 = 24, so x = 12 (and y = 3).
7. Solve the simultaneous equations x + y = 41 and x − y = 9. Find the value of x.
25
Add the two equations: 2x = 41 + 9 = 50, so x = 25 (and y = 16).
8. Solve the simultaneous equations x + y = 31 and x − y = 19. Find the value of x.
25
Add the two equations: 2x = 31 + 19 = 50, so x = 25 (and y = 6).
9. Solve the simultaneous equations x + y = 16 and x − y = 14. Find the value of x.
15
Add the two equations: 2x = 16 + 14 = 30, so x = 15 (and y = 1).
10. Solve the simultaneous equations x + y = 11 and x − y = 3. Find the value of x.
7
Add the two equations: 2x = 11 + 3 = 14, so x = 7 (and y = 4).
11. Solve the simultaneous equations x + y = 26 and x − y = 16. Find the value of x.
21
Add the two equations: 2x = 26 + 16 = 42, so x = 21 (and y = 5).
12. Solve the simultaneous equations x + y = 33 and x − y = 3. Find the value of x.
18
Add the two equations: 2x = 33 + 3 = 36, so x = 18 (and y = 15).

12 questions · Seed 104737 · Age guidance, not curriculum certification