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Welcome to GCSE Edexcel Maths revision.

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Topic M 16: Simultaneous equations.

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This video covers Higher tier.

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It includes the shared content and the labelled Higher extensions.

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Simultaneous equations must both be true for the same pair of values.

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Their solution is the intersection of their graphs.

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Intersection of x plus y equals seven and x minus y equals one

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Elimination adds or subtracts equations to remove a variable.

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If its coefficients are equal, subtract; if they are opposites, add.

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Worked example: x plus y equals 7 and x minus y equals 1.

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Add to get 2 x equals 8, so x equals 4.

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Substitute into x plus y equals 7 to obtain y equals 3.

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Worked example: 2 x plus 3 y equals 13 and 3 x plus 2 y equals 12.

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Multiply the first by 3 and the second by 2 to obtain 6 x plus 9 y equals 39 and 6 x plus 4 y equals 24.

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Subtract: 5 y equals 15, so y equals 3 and x equals 2.

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When multiplying an equation, multiply every term on both sides.

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Keep negative signs and the equals sign aligned when eliminating.

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Substitution is useful if one variable is already isolated.

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From y equals 2 x plus 1 and x plus y equals 10, substitute: x plus 2 x plus 1 equals 10, giving x equals 3 and y equals 7.

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Check a candidate pair in both original equations.

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Satisfying one equation alone is not enough.

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Worked example: Two adult and three child tickets cost 31 pounds; three adult and two child tickets cost 34 pounds.

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Set 2 a plus 3 c equals 31 and 3 a plus 2 c equals 34.

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Eliminating gives c equals 5 pounds and a equals 8 pounds.

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Graphical intersections give approximate solutions limited by scale.

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Parallel distinct lines have no solution; equations describing the same line have infinitely many pairs.

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Define the variables with units before modelling, and interpret the pair in the context rather than reporting bare x and y values.

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Substitute the linear expression into the quadratic equation to obtain an equation in one variable.

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Solve it, then recover the other coordinate for each root.

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Worked example: y equals x plus 2 and y equals x squared .

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Set x squared equals x plus 2, giving open bracket x minus 2 close bracket multiplied by open bracket x plus 1 close bracket equals 0.

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The solutions are open bracket 2, 4 close bracket and open bracket minus 1, 1 close bracket .

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Intersections of y equals x plus two and y equals x squared

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For x squared plus y squared equals 25 and y equals x plus 1, substitute the whole bracket: x squared plus open bracket x plus 1 close bracket squared equals 25.

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Expand before solving; open bracket x plus 1 close bracket squared is not x squared plus 1.

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A line can meet a parabola or circle twice, once or not at all.

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Keep corresponding x and y values paired; do not mix coordinates from different solutions.

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That completes Simultaneous equations.

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Revisit the notes and test yourself on the revision website.