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 = 28 and x − y = 18. Find the value of x.
28 · 18 · Simultaneous linear equati…
2. Solve the simultaneous equations x + y = 38 and x − y = 10. Find the value of x.
38 · 10 · Simultaneous linear equati…
3. Solve the simultaneous equations x + y = 32 and x − y = 6. Find the value of x.
32 · 6 · Simultaneous linear equati…
4. Solve the simultaneous equations x + y = 14 and x − y = 4. Find the value of x.
14 · 4 · Simultaneous linear equati…
5. Solve the simultaneous equations x + y = 19 and x − y = 9. Find the value of x.
19 · 9 · Simultaneous linear equati…
6. Solve the simultaneous equations x + y = 8 and x − y = 4. Find the value of x.
8 · 4 · Simultaneous linear equati…
7. Solve the simultaneous equations x + y = 9 and x − y = 3. Find the value of x.
9 · 3 · Simultaneous linear equati…
8. Solve the simultaneous equations x + y = 23 and x − y = 3. Find the value of x.
23 · 3 · Simultaneous linear equati…
9. Solve the simultaneous equations x + y = 32 and x − y = 10. Find the value of x.
32 · 10 · Simultaneous linear equati…
10. Solve the simultaneous equations x + y = 6 and x − y = 4. Find the value of x.
6 · 4 · Simultaneous linear equati…
11. Solve the simultaneous equations x + y = 17 and x − y = 15. Find the value of x.
17 · 15 · Simultaneous linear equati…
12. Solve the simultaneous equations x + y = 12 and x − y = 2. Find the value of x.
12 · 2 · Simultaneous linear equati…

12 questions · Seed 42 · 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 = 28 and x − y = 18. Find the value of x.
23
Add the two equations: 2x = 28 + 18 = 46, so x = 23 (and y = 5).
2. Solve the simultaneous equations x + y = 38 and x − y = 10. Find the value of x.
24
Add the two equations: 2x = 38 + 10 = 48, so x = 24 (and y = 14).
3. Solve the simultaneous equations x + y = 32 and x − y = 6. Find the value of x.
19
Add the two equations: 2x = 32 + 6 = 38, so x = 19 (and y = 13).
4. Solve the simultaneous equations x + y = 14 and x − y = 4. Find the value of x.
9
Add the two equations: 2x = 14 + 4 = 18, so x = 9 (and y = 5).
5. Solve the simultaneous equations x + y = 19 and x − y = 9. Find the value of x.
14
Add the two equations: 2x = 19 + 9 = 28, so x = 14 (and y = 5).
6. Solve the simultaneous equations x + y = 8 and x − y = 4. Find the value of x.
6
Add the two equations: 2x = 8 + 4 = 12, so x = 6 (and y = 2).
7. Solve the simultaneous equations x + y = 9 and x − y = 3. Find the value of x.
6
Add the two equations: 2x = 9 + 3 = 12, so x = 6 (and y = 3).
8. Solve the simultaneous equations x + y = 23 and x − y = 3. Find the value of x.
13
Add the two equations: 2x = 23 + 3 = 26, so x = 13 (and y = 10).
9. Solve the simultaneous equations x + y = 32 and x − y = 10. Find the value of x.
21
Add the two equations: 2x = 32 + 10 = 42, so x = 21 (and y = 11).
10. Solve the simultaneous equations x + y = 6 and x − y = 4. Find the value of x.
5
Add the two equations: 2x = 6 + 4 = 10, so x = 5 (and y = 1).
11. Solve the simultaneous equations x + y = 17 and x − y = 15. Find the value of x.
16
Add the two equations: 2x = 17 + 15 = 32, so x = 16 (and y = 1).
12. Solve the simultaneous equations x + y = 12 and x − y = 2. Find the value of x.
7
Add the two equations: 2x = 12 + 2 = 14, so x = 7 (and y = 5).

12 questions · Seed 42 · 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 = 28 and x − y = 18. Find the value of x.
28 · 18 · Simultaneous linear equati…
2. Solve the simultaneous equations x + y = 38 and x − y = 10. Find the value of x.
38 · 10 · Simultaneous linear equati…
3. Solve the simultaneous equations x + y = 32 and x − y = 6. Find the value of x.
32 · 6 · Simultaneous linear equati…
4. Solve the simultaneous equations x + y = 14 and x − y = 4. Find the value of x.
14 · 4 · Simultaneous linear equati…
5. Solve the simultaneous equations x + y = 19 and x − y = 9. Find the value of x.
19 · 9 · Simultaneous linear equati…
6. Solve the simultaneous equations x + y = 8 and x − y = 4. Find the value of x.
8 · 4 · Simultaneous linear equati…
7. Solve the simultaneous equations x + y = 9 and x − y = 3. Find the value of x.
9 · 3 · Simultaneous linear equati…
8. Solve the simultaneous equations x + y = 23 and x − y = 3. Find the value of x.
23 · 3 · Simultaneous linear equati…
9. Solve the simultaneous equations x + y = 32 and x − y = 10. Find the value of x.
32 · 10 · Simultaneous linear equati…
10. Solve the simultaneous equations x + y = 6 and x − y = 4. Find the value of x.
6 · 4 · Simultaneous linear equati…
11. Solve the simultaneous equations x + y = 17 and x − y = 15. Find the value of x.
17 · 15 · Simultaneous linear equati…
12. Solve the simultaneous equations x + y = 12 and x − y = 2. Find the value of x.
12 · 2 · Simultaneous linear equati…

12 questions · Seed 42 · 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 = 28 and x − y = 18. Find the value of x.
23
Add the two equations: 2x = 28 + 18 = 46, so x = 23 (and y = 5).
2. Solve the simultaneous equations x + y = 38 and x − y = 10. Find the value of x.
24
Add the two equations: 2x = 38 + 10 = 48, so x = 24 (and y = 14).
3. Solve the simultaneous equations x + y = 32 and x − y = 6. Find the value of x.
19
Add the two equations: 2x = 32 + 6 = 38, so x = 19 (and y = 13).
4. Solve the simultaneous equations x + y = 14 and x − y = 4. Find the value of x.
9
Add the two equations: 2x = 14 + 4 = 18, so x = 9 (and y = 5).
5. Solve the simultaneous equations x + y = 19 and x − y = 9. Find the value of x.
14
Add the two equations: 2x = 19 + 9 = 28, so x = 14 (and y = 5).
6. Solve the simultaneous equations x + y = 8 and x − y = 4. Find the value of x.
6
Add the two equations: 2x = 8 + 4 = 12, so x = 6 (and y = 2).
7. Solve the simultaneous equations x + y = 9 and x − y = 3. Find the value of x.
6
Add the two equations: 2x = 9 + 3 = 12, so x = 6 (and y = 3).
8. Solve the simultaneous equations x + y = 23 and x − y = 3. Find the value of x.
13
Add the two equations: 2x = 23 + 3 = 26, so x = 13 (and y = 10).
9. Solve the simultaneous equations x + y = 32 and x − y = 10. Find the value of x.
21
Add the two equations: 2x = 32 + 10 = 42, so x = 21 (and y = 11).
10. Solve the simultaneous equations x + y = 6 and x − y = 4. Find the value of x.
5
Add the two equations: 2x = 6 + 4 = 10, so x = 5 (and y = 1).
11. Solve the simultaneous equations x + y = 17 and x − y = 15. Find the value of x.
16
Add the two equations: 2x = 17 + 15 = 32, so x = 16 (and y = 1).
12. Solve the simultaneous equations x + y = 12 and x − y = 2. Find the value of x.
7
Add the two equations: 2x = 12 + 2 = 14, so x = 7 (and y = 5).

12 questions · Seed 42 · Age guidance, not curriculum certification