Ceist Eile

Ceist Eile is in development. Features, questions and prices may change while we refine it.

Junior Cycle · Junior Cycle Maths

Junior Cycle Maths: Linear & simultaneous equations

How often Linear & simultaneous equations comes up on the Maths papers, every year it was asked, and questions to try.

HL Asked on 5 of the last 5 Higher Level papers, most recently in 2026. banker

OL Asked on 5 of the last 5 Ordinary Level papers, most recently in 2026. banker

Linear & simultaneous equations, Higher Level(8 marks)

Quick ones on Linear & simultaneous equations.

(a)Solve 5x − 7 = 2x + 8.
  1. x = 15
  2. x = 5
  3. x = 1/3
(b)Solve 3(x − 2) = 5 − (x + 3).
  1. x = −1
  2. x = 3.5
  3. x = 2
(c)Solve (x + 2)/3 − (x − 1)/4 = 1.
  1. x = 1
  2. x = 23
  3. x = 7
Show the answers

(a) x = 5

(b) x = 2

(c) x = 1

Your turn: Higher Level questions on Linear & simultaneous equations.

Higher Level

Asked on 5 of the last 5 Higher Level papers, most recently in 2026. banker

Every paper, year by year

YearWhere it came up
2026Q7
2025Q10, Q12
2024Q7
2023Q10
2022Q4

Links open the State Examinations Commission’s paper for that year.

Ordinary Level

Asked on 5 of the last 5 Ordinary Level papers, most recently in 2026. banker

Every paper, year by year

YearWhere it came up
2026Q6
2025Q7, Q10
2024Q7
2023Q2, Q12
2022Q10

Links open the State Examinations Commission’s paper for that year.

More Linear & simultaneous equations questions

Linear & simultaneous equations, 2 marks

Solve 3x − 4 = 11.

  1. x = 15
  2. x = 7/3
  3. x = 5
Show the answer

x = 5

Add 4 to both sides: 3x = 15. Divide both sides by 3: x = 5. Check: 3(5) − 4 = 11.

Linear & simultaneous equations, 3 marks

Solve the simultaneous equations x + y = 10 and x − y = 4.

  1. x = 6, y = 4
  2. x = 7, y = 3
  3. x = 3, y = 7
Show the answer

x = 7, y = 3

Add the two equations: 2x = 14, so x = 7. Then 7 + y = 10 gives y = 3. Check in the other one: 7 − 3 = 4.

Linear & simultaneous equations, 3 marks

Solve 5x + 2 = 2x + 14.

  1. x = 4
  2. x = 12
  3. x = 16/3
Show the answer

x = 4

Take 2x from both sides: 3x + 2 = 14. Take 2 from both sides: 3x = 12. Divide by 3: x = 4. Check: 22 = 22.

Other Maths topics

All of Junior Cycle Maths