GCSE Maths: Simultaneous Equations Made Simple

Simultaneous equations come up a lot in GCSE Maths and they are very scoreable once your method is tidy. This guide gives you the exact process to use in exams.

What are simultaneous equations?

They are two equations with the same unknowns, usually x and y. You need values that satisfy both equations at the same time.

Method 1: Elimination

Example:
2x + y = 11
x - y = 1

1. Add the equations to eliminate y:
   (2x + y) + (x - y) = 11 + 1 => 3x = 12
2. Solve: x = 4
3. Substitute into x - y = 1:
   4 - y = 1 => y = 3

Answer: x = 4, y = 3

Method 2: Substitution

Example:
y = 2x + 1
x + y = 10

1. Substitute y into second equation:
   x + (2x + 1) = 10
2. Solve: 3x + 1 = 10 => 3x = 9 => x = 3
3. Find y: y = 2(3) + 1 = 7

Answer: x = 3, y = 7

Common mistakes

• Sign errors when moving terms
• Forgetting to substitute back for the second variable
• Not checking the pair in both equations

Exam tip

If coefficients are close, elimination is usually quicker. If one equation is already rearranged (like y = ...), substitution is often cleaner.

Quick check routine

1. Put your answers into equation 1
2. Put your answers into equation 2
3. If both match, bank the marks

Keep your lines clear and methodical and this topic becomes free marks.