IGCSE Math RevisionWorked example 1: Elimination
Solve \(2x+3y=12\) and \(4x-3y=6\).
Solution
- Add the equations (the \(y\) terms cancel): \(6x=18\), so \(x=3\).
- Substitute: \(6+3y=12\), so \(y=2\).
Answer: \(x=3,\ y=2\)
Tip: Same signs subtract, different signs add.
Edexcel IGCSE Maths (4MA1) · Unit 3: Equations & Sequences
IGCSE Maths Simultaneous Equations Questions and Answers
Simultaneous Equations questions with full solutions for Pearson Edexcel International GCSE Mathematics A (4MA1), Higher tier. Read the 5 worked examples first, then try the 3 exam-style questions yourself and check your working against the mark scheme.
- 5 worked examples
- 3 questions with mark schemes
- Higher tier · calculator allowed
- Free, no sign-in
What this topic covers
- Equations 6: Simultaneous equations by substitution.
- Equations 7: Simultaneous equations from word problems.
- Quadratic Simultaneous Equations 1: One linear + one quadratic equation solved together.
- Quadratic Simultaneous Equations 2: Simultaneous where both curves are quadratic.
- Quadratic Simultaneous Equations 3: Modelling simultaneous problems with quadratics.
Simultaneous Equations worked examples
Worked example 2: Substitution
Solve \(y=3x-1\) and \(2x+y=9\).
Solution
- Substitute: \(2x+3x-1=9\).
- \(5x=10\), so \(x=2\) and \(y=5\).
Answer: \(x=2,\ y=5\)
Tip: Check in both equations.
Worked example 3: Line and circle
Solve \(y=x-1\) and \(x^2+y^2=13\).
Solution
- Substitute: \(x^2+(x-1)^2=13\).
- \(2x^2-2x-12=0\), so \(x^2-x-6=0\).
- \((x-3)(x+2)=0\): \(x=3,\ y=2\) or \(x=-2,\ y=-3\).
Answer: \((3,\ 2)\) and \((-2,\ -3)\)
Tip: Pair each x with its own y.
Worked example 4: Line and parabola
Solve \(y=x^2+2\) and \(y=3x\).
Solution
- \(x^2+2=3x\), so \(x^2-3x+2=0\).
- \((x-1)(x-2)=0\).
- \((1,\ 3)\) and \((2,\ 6)\).
Answer: \((1,\ 3)\) and \((2,\ 6)\)
Tip: Use the linear equation to find y.
Worked example 5: Product and sum
Solve \(xy=12\) and \(x+y=7\).
Solution
- \(y=7-x\), so \(x(7-x)=12\).
- \(x^2-7x+12=0\), \((x-3)(x-4)=0\).
- \(x=3,\ y=4\) or \(x=4,\ y=3\).
Answer: \((3,4)\) and \((4,3)\)
Tip: Rearrange the linear equation first.
Simultaneous Equations exam-style questions
Try each question before you open the answer. The mark schemes use Edexcel-style marks: M for method, A for accuracy (after the method mark), B for an independent result.
Question 1
Solve the simultaneous equations \( 2x + 5y = 1 \) and \( 4x - 5y = 17 \).
Show the answer and mark scheme
- M1 adds to eliminate y: 6x = 18
- M1 substitutes their x = 3 into either equation
- A1 x = 3, y = −1
Answer: \( x = 3 \), \( y = -1 \)
Question 2
Solve the simultaneous equations \( 4x + 3y = 25 \) and \( 3x + 2y = 18 \).
Show the answer and mark scheme
- M1 multiplies to match coefficients, e.g. 8x + 6y = 50 and 9x + 6y = 54
- M1 eliminates a variable and substitutes back
- A1 x = 4, y = 3
Answer: \( x = 4 \), \( y = 3 \)
Question 3
At a climbing centre, 3 adult sessions and 5 junior sessions cost £65.75 in total. 4 adult sessions and 2 junior sessions cost £58.50 in total. Work out the cost of one adult session and the cost of one junior session.
Show the answer and mark scheme
- M1 3a + 5j = 65.75 and 4a + 2j = 58.50
- M1 matches coefficients and eliminates, e.g. 12a + 20j = 263 and 12a + 6j = 175.50
- A1 j = 6.25 or a = 11.50
- A1 adult £11.50, junior £6.25
Answer: adult £11.50, junior £6.25
Every question and worked example here is original, written for IGCSE Math Revision rather than copied from Pearson papers, and each answer was re-solved independently before publishing.
Revise simultaneous equations for the exam
- Unit 3 practice: Equations & Sequences in the student hub (more questions with mark schemes)
- IGCSE Maths revision notes for this topic and the IGCSE Maths formula sheet
- Edexcel IGCSE Maths 4MA1 past papers to practise under exam conditions
- IGCSE Maths 4MA1 examiner report summary: where students lose marks
Questions students ask
Which Edexcel IGCSE Maths papers test simultaneous equations?
Either Higher tier paper, 1H or 2H, can test simultaneous equations: both cover the whole Pearson Edexcel International GCSE Mathematics A (4MA1) specification and both allow a calculator. Show your method, because most marks are for working.
Where can I practise more simultaneous equations questions?
In the IGCSE student hub: Unit 3 (Equations & Sequences) has more exam-style questions on this topic, each with a mark scheme. Practice starts with a 7-day free trial; the worked examples and questions on this page are free.