Simultaneous Equations
Solve a pair of linear simultaneous equations by elimination and by substitution.
Overview
Simultaneous equations are two equations with two unknowns that are true at the same time. In Year 9 students solve them by elimination (adding or subtracting the equations) and by substitution, and use them to solve real problems. This is a core IGCSE Algebra skill and a favourite of examiners.
What You Will Learn
- Understand what a pair of simultaneous equations represents
- Solve simultaneous equations by elimination
- Solve simultaneous equations by substitution
- Check a solution by substituting back into both equations
- Form and solve simultaneous equations from a word problem
Key Vocabulary
Common Mistakes to Avoid
- Adding the equations when you should subtract to eliminate a variable (or vice versa)
- Making a sign error when subtracting one equation from another
- Finding one unknown but forgetting to find the other
- Not checking the solution in both original equations
What Comes Next
At IGCSE this extends to harder coefficients, solving by graph, and to one linear and one non-linear equation, within the Algebra and Graphs topic.
Frequently Asked Questions
When do I add and when do I subtract the equations?
Look at the matching terms. If they have the same sign and equal coefficient, subtract to eliminate them; if they have opposite signs, add. The aim is to cancel one of the unknowns so you are left with a single equation.
What does the solution to simultaneous equations mean?
It is the pair of values (one for each unknown) that makes both equations true at the same time. Graphically, it is the point where the two lines cross.
Study This Topic
Topic Details
- Stage
- Year 9
- Strand
- Algebra
- Framework ref
- 9Ae
- Difficulty
- High
Build strong foundations in Simultaneous Equations
A free trial class with Teacher Rig helps your Year 9 child master Simultaneous Equations now — so IGCSE Maths feels familiar, not frightening, later.
Heading toward IGCSE? See how Simultaneous Equations develops in IGCSE Algebra and Graphs (Cambridge 0580) →