Simultaneous Equations
AQA Mathematicsintermediate⭐ High PriorityYears 10-11
What You Need to Know
- Two equations with two unknowns — find values that satisfy BOTH
- Two main methods: elimination and substitution
- Elimination: add/subtract equations to remove one variable
- Substitution: rearrange one equation and substitute into the other
Elimination Method
Multiply one or both equations so that the coefficients of one variable match, then add or subtract to eliminate it.
Worked Example
Solve: 3x + 2y = 12 and x + 2y = 8
Both equations have 2y — subtract equation 2 from equation 1(3x + 2y) - (x + 2y) = 12 - 82x = 4, so x = 2Substitute x = 2 into second equation: 2 + 2y = 8, so y = 3
Answer: x = 2, y = 3
Common Mistakes
- Forgetting to multiply ALL terms when scaling an equation
- Getting the sign wrong when subtracting equations
- Only finding one variable and forgetting to find the other
Exam Tips
- Always check your answer by substituting back into BOTH original equations
- If asked to solve graphically, the solution is where the lines cross
Related Topics
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