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 = 33 and x − y = 3. Find the value of x.
33 · 3 · Simultaneous linear equati…
2. Solve the simultaneous equations x + y = 13 and x − y = 1. Find the value of x.
13 · 1 · Simultaneous linear equati…
3. Solve the simultaneous equations x + y = 12 and x − y = 6. Find the value of x.
12 · 6 · Simultaneous linear equati…
4. Solve the simultaneous equations x + y = 41 and x − y = 9. Find the value of x.
41 · 9 · Simultaneous linear equati…
5. Solve the simultaneous equations x + y = 8 and x − y = 6. Find the value of x.
8 · 6 · Simultaneous linear equati…
6. Solve the simultaneous equations x + y = 22 and x − y = 6. Find the value of x.
22 · 6 · Simultaneous linear equati…
7. Solve the simultaneous equations x + y = 30 and x − y = 10. Find the value of x.
30 · 10 · Simultaneous linear equati…
8. Solve the simultaneous equations x + y = 24 and x − y = 12. Find the value of x.
24 · 12 · Simultaneous linear equati…
9. Solve the simultaneous equations x + y = 9 and x − y = 1. Find the value of x.
9 · 1 · Simultaneous linear equati…
10. Solve the simultaneous equations x + y = 41 and x − y = 7. Find the value of x.
41 · 7 · Simultaneous linear equati…
11. Solve the simultaneous equations x + y = 37 and x − y = 3. Find the value of x.
37 · 3 · Simultaneous linear equati…
12. Solve the simultaneous equations x + y = 15 and x − y = 3. Find the value of x.
15 · 3 · Simultaneous linear equati…

12 questions · Seed 44 · 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 = 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).
2. 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).
3. Solve the simultaneous equations x + y = 12 and x − y = 6. Find the value of x.
9
Add the two equations: 2x = 12 + 6 = 18, so x = 9 (and y = 3).
4. 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).
5. Solve the simultaneous equations x + y = 8 and x − y = 6. Find the value of x.
7
Add the two equations: 2x = 8 + 6 = 14, so x = 7 (and y = 1).
6. Solve the simultaneous equations x + y = 22 and x − y = 6. Find the value of x.
14
Add the two equations: 2x = 22 + 6 = 28, so x = 14 (and y = 8).
7. Solve the simultaneous equations x + y = 30 and x − y = 10. Find the value of x.
20
Add the two equations: 2x = 30 + 10 = 40, so x = 20 (and y = 10).
8. Solve the simultaneous equations x + y = 24 and x − y = 12. Find the value of x.
18
Add the two equations: 2x = 24 + 12 = 36, so x = 18 (and y = 6).
9. Solve the simultaneous equations x + y = 9 and x − y = 1. Find the value of x.
5
Add the two equations: 2x = 9 + 1 = 10, so x = 5 (and y = 4).
10. Solve the simultaneous equations x + y = 41 and x − y = 7. Find the value of x.
24
Add the two equations: 2x = 41 + 7 = 48, so x = 24 (and y = 17).
11. Solve the simultaneous equations x + y = 37 and x − y = 3. Find the value of x.
20
Add the two equations: 2x = 37 + 3 = 40, so x = 20 (and y = 17).
12. Solve the simultaneous equations x + y = 15 and x − y = 3. Find the value of x.
9
Add the two equations: 2x = 15 + 3 = 18, so x = 9 (and y = 6).

12 questions · Seed 44 · 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 = 33 and x − y = 3. Find the value of x.
33 · 3 · Simultaneous linear equati…
2. Solve the simultaneous equations x + y = 13 and x − y = 1. Find the value of x.
13 · 1 · Simultaneous linear equati…
3. Solve the simultaneous equations x + y = 12 and x − y = 6. Find the value of x.
12 · 6 · Simultaneous linear equati…
4. Solve the simultaneous equations x + y = 41 and x − y = 9. Find the value of x.
41 · 9 · Simultaneous linear equati…
5. Solve the simultaneous equations x + y = 8 and x − y = 6. Find the value of x.
8 · 6 · Simultaneous linear equati…
6. Solve the simultaneous equations x + y = 22 and x − y = 6. Find the value of x.
22 · 6 · Simultaneous linear equati…
7. Solve the simultaneous equations x + y = 30 and x − y = 10. Find the value of x.
30 · 10 · Simultaneous linear equati…
8. Solve the simultaneous equations x + y = 24 and x − y = 12. Find the value of x.
24 · 12 · Simultaneous linear equati…
9. Solve the simultaneous equations x + y = 9 and x − y = 1. Find the value of x.
9 · 1 · Simultaneous linear equati…
10. Solve the simultaneous equations x + y = 41 and x − y = 7. Find the value of x.
41 · 7 · Simultaneous linear equati…
11. Solve the simultaneous equations x + y = 37 and x − y = 3. Find the value of x.
37 · 3 · Simultaneous linear equati…
12. Solve the simultaneous equations x + y = 15 and x − y = 3. Find the value of x.
15 · 3 · Simultaneous linear equati…

12 questions · Seed 44 · 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 = 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).
2. 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).
3. Solve the simultaneous equations x + y = 12 and x − y = 6. Find the value of x.
9
Add the two equations: 2x = 12 + 6 = 18, so x = 9 (and y = 3).
4. 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).
5. Solve the simultaneous equations x + y = 8 and x − y = 6. Find the value of x.
7
Add the two equations: 2x = 8 + 6 = 14, so x = 7 (and y = 1).
6. Solve the simultaneous equations x + y = 22 and x − y = 6. Find the value of x.
14
Add the two equations: 2x = 22 + 6 = 28, so x = 14 (and y = 8).
7. Solve the simultaneous equations x + y = 30 and x − y = 10. Find the value of x.
20
Add the two equations: 2x = 30 + 10 = 40, so x = 20 (and y = 10).
8. Solve the simultaneous equations x + y = 24 and x − y = 12. Find the value of x.
18
Add the two equations: 2x = 24 + 12 = 36, so x = 18 (and y = 6).
9. Solve the simultaneous equations x + y = 9 and x − y = 1. Find the value of x.
5
Add the two equations: 2x = 9 + 1 = 10, so x = 5 (and y = 4).
10. Solve the simultaneous equations x + y = 41 and x − y = 7. Find the value of x.
24
Add the two equations: 2x = 41 + 7 = 48, so x = 24 (and y = 17).
11. Solve the simultaneous equations x + y = 37 and x − y = 3. Find the value of x.
20
Add the two equations: 2x = 37 + 3 = 40, so x = 20 (and y = 17).
12. Solve the simultaneous equations x + y = 15 and x − y = 3. Find the value of x.
9
Add the two equations: 2x = 15 + 3 = 18, so x = 9 (and y = 6).

12 questions · Seed 44 · Age guidance, not curriculum certification