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.

New variation Try interactive challenge Browse templates

Age band:Ages 13-15 Ages 16-18

Choose “Save as PDF” to keep a copy. Use your browser’s paper setting for A4 or Letter.

Worksheet StudioPractice pack · Ages 13-15

Simultaneous linear equations

Take your time. Show your thinking.

1. Solve the simultaneous equations x + y = 34 and x − y = 6. Find the value of x.
34 · 6 · Simultaneous linear equati…
2. Solve the simultaneous equations x + y = 6 and x − y = 4. Find the value of x.
6 · 4 · Simultaneous linear equati…
3. Solve the simultaneous equations x + y = 10 and x − y = 4. Find the value of x.
10 · 4 · Simultaneous linear equati…
4. Solve the simultaneous equations x + y = 28 and x − y = 2. Find the value of x.
28 · 2 · Simultaneous linear equati…
5. Solve the simultaneous equations x + y = 36 and x − y = 10. Find the value of x.
36 · 10 · Simultaneous linear equati…
6. Solve the simultaneous equations x + y = 26 and x − y = 22. Find the value of x.
26 · 22 · Simultaneous linear equati…
7. Solve the simultaneous equations x + y = 33 and x − y = 11. Find the value of x.
33 · 11 · Simultaneous linear equati…
8. Solve the simultaneous equations x + y = 19 and x − y = 9. Find the value of x.
19 · 9 · Simultaneous linear equati…
9. Solve the simultaneous equations x + y = 28 and x − y = 10. Find the value of x.
28 · 10 · Simultaneous linear equati…
10. Solve the simultaneous equations x + y = 20 and x − y = 4. Find the value of x.
20 · 4 · Simultaneous linear equati…
11. Solve the simultaneous equations x + y = 36 and x − y = 14. Find the value of x.
36 · 14 · Simultaneous linear equati…
12. Solve the simultaneous equations x + y = 25 and x − y = 13. Find the value of x.
25 · 13 · Simultaneous linear equati…

12 questions · Seed 104732 · 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 = 34 and x − y = 6. Find the value of x.
20
Add the two equations: 2x = 34 + 6 = 40, so x = 20 (and y = 14).
2. 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).
3. Solve the simultaneous equations x + y = 10 and x − y = 4. Find the value of x.
7
Add the two equations: 2x = 10 + 4 = 14, so x = 7 (and y = 3).
4. Solve the simultaneous equations x + y = 28 and x − y = 2. Find the value of x.
15
Add the two equations: 2x = 28 + 2 = 30, so x = 15 (and y = 13).
5. Solve the simultaneous equations x + y = 36 and x − y = 10. Find the value of x.
23
Add the two equations: 2x = 36 + 10 = 46, so x = 23 (and y = 13).
6. Solve the simultaneous equations x + y = 26 and x − y = 22. Find the value of x.
24
Add the two equations: 2x = 26 + 22 = 48, so x = 24 (and y = 2).
7. Solve the simultaneous equations x + y = 33 and x − y = 11. Find the value of x.
22
Add the two equations: 2x = 33 + 11 = 44, so x = 22 (and y = 11).
8. 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).
9. Solve the simultaneous equations x + y = 28 and x − y = 10. Find the value of x.
19
Add the two equations: 2x = 28 + 10 = 38, so x = 19 (and y = 9).
10. Solve the simultaneous equations x + y = 20 and x − y = 4. Find the value of x.
12
Add the two equations: 2x = 20 + 4 = 24, so x = 12 (and y = 8).
11. Solve the simultaneous equations x + y = 36 and x − y = 14. Find the value of x.
25
Add the two equations: 2x = 36 + 14 = 50, so x = 25 (and y = 11).
12. Solve the simultaneous equations x + y = 25 and x − y = 13. Find the value of x.
19
Add the two equations: 2x = 25 + 13 = 38, so x = 19 (and y = 6).

12 questions · Seed 104732 · 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 = 34 and x − y = 6. Find the value of x.
34 · 6 · Simultaneous linear equati…
2. Solve the simultaneous equations x + y = 6 and x − y = 4. Find the value of x.
6 · 4 · Simultaneous linear equati…
3. Solve the simultaneous equations x + y = 10 and x − y = 4. Find the value of x.
10 · 4 · Simultaneous linear equati…
4. Solve the simultaneous equations x + y = 28 and x − y = 2. Find the value of x.
28 · 2 · Simultaneous linear equati…
5. Solve the simultaneous equations x + y = 36 and x − y = 10. Find the value of x.
36 · 10 · Simultaneous linear equati…
6. Solve the simultaneous equations x + y = 26 and x − y = 22. Find the value of x.
26 · 22 · Simultaneous linear equati…
7. Solve the simultaneous equations x + y = 33 and x − y = 11. Find the value of x.
33 · 11 · Simultaneous linear equati…
8. Solve the simultaneous equations x + y = 19 and x − y = 9. Find the value of x.
19 · 9 · Simultaneous linear equati…
9. Solve the simultaneous equations x + y = 28 and x − y = 10. Find the value of x.
28 · 10 · Simultaneous linear equati…
10. Solve the simultaneous equations x + y = 20 and x − y = 4. Find the value of x.
20 · 4 · Simultaneous linear equati…
11. Solve the simultaneous equations x + y = 36 and x − y = 14. Find the value of x.
36 · 14 · Simultaneous linear equati…
12. Solve the simultaneous equations x + y = 25 and x − y = 13. Find the value of x.
25 · 13 · Simultaneous linear equati…

12 questions · Seed 104732 · 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 = 34 and x − y = 6. Find the value of x.
20
Add the two equations: 2x = 34 + 6 = 40, so x = 20 (and y = 14).
2. 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).
3. Solve the simultaneous equations x + y = 10 and x − y = 4. Find the value of x.
7
Add the two equations: 2x = 10 + 4 = 14, so x = 7 (and y = 3).
4. Solve the simultaneous equations x + y = 28 and x − y = 2. Find the value of x.
15
Add the two equations: 2x = 28 + 2 = 30, so x = 15 (and y = 13).
5. Solve the simultaneous equations x + y = 36 and x − y = 10. Find the value of x.
23
Add the two equations: 2x = 36 + 10 = 46, so x = 23 (and y = 13).
6. Solve the simultaneous equations x + y = 26 and x − y = 22. Find the value of x.
24
Add the two equations: 2x = 26 + 22 = 48, so x = 24 (and y = 2).
7. Solve the simultaneous equations x + y = 33 and x − y = 11. Find the value of x.
22
Add the two equations: 2x = 33 + 11 = 44, so x = 22 (and y = 11).
8. 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).
9. Solve the simultaneous equations x + y = 28 and x − y = 10. Find the value of x.
19
Add the two equations: 2x = 28 + 10 = 38, so x = 19 (and y = 9).
10. Solve the simultaneous equations x + y = 20 and x − y = 4. Find the value of x.
12
Add the two equations: 2x = 20 + 4 = 24, so x = 12 (and y = 8).
11. Solve the simultaneous equations x + y = 36 and x − y = 14. Find the value of x.
25
Add the two equations: 2x = 36 + 14 = 50, so x = 25 (and y = 11).
12. Solve the simultaneous equations x + y = 25 and x − y = 13. Find the value of x.
19
Add the two equations: 2x = 25 + 13 = 38, so x = 19 (and y = 6).

12 questions · Seed 104732 · Age guidance, not curriculum certification