IGCSE Maths / Simultaneous equations
Simultaneous equations by elimination revision notes
Edexcel International GCSE Maths (4MA1), chapter 7: Simultaneous equations, specification point 2.6a. Free lesson.
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Elimination solves simultaneous equations by making one pair of terms match, then adding or subtracting to remove that unknown. Find both values exactly and check them in the equation you did not use.
What simultaneous equations mean
Both equations must be true for the same pair of numbers. In an equation such as 4x + 3y = 25, the numbers multiplying the letters are called coefficients. Elimination removes one letter so you can solve for the other. The solution is a pair of values for x and y. Exact answers are whole numbers or fractions, not rounded decimals.
When the terms already match
If the same letter has matching coefficients, add or subtract the equations to remove it. Choose the operation using the signs: same signs cancel when you subtract, while opposite signs cancel when you add. Number the equations (1) and (2), and label each new line. Clear working helps you earn method marks.
Choose the operation that cancels
Adding and subtracting are not interchangeable. The signs of the matching terms tell you which operation removes them. 4y − (−4y) = 8y, so subtracting opposite terms makes them add together. 4y + (−4y) = 0, so adding opposite terms removes them. The same rule applies to any matching pair of terms.
When you need to multiply first
If no pair of coefficients matches, multiply every term in one equation until a pair does. Include the number on the right-hand side. Then use the signs of the matched terms to decide whether to add or subtract. For example, doubling −2y gives −4y, which matches 4y with the opposite sign. Opposite signs mean you add the equations.
Finish by checking
After finding both values, substitute them into the equation you did not use to find the second value. If the left side gives the stated right side, the pair works in both equations. The final answer must give both values, for example x = 4 and y = 3.