Simultaneous Equations (Edexcel IGCSE Maths A)

Linear simultaneous equations are equations with two unknowns (say x and y) where the terms have variables with no powers higher than 1 (so no x², y², xy, etc.).

The elimination method completely removes one of the variables, x or y, from the simultaneous equations by adding or subtracting the equations (after multiplying them by suitable constants if necessary).

The substitution method involves rearranging one equation to make one variable (x or y) the subject, and then substituting this expression into the other equation to eliminate that variable.

To solve linear simultaneous equations using a graph, plot both equations on the same set of axes and find the point of intersection. The x- and y- coordinates of that point give the solutions for x and y.

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Always check that your final solutions satisfy the original simultaneous equations.

Quadratic simultaneous equations are simultaneous equations where at least one equation contains a squared term (x² or y² or xy).

The method used for solving quadratic simultaneous equations is substitution.

To use substitution to solve quadratic simultaneous equations:

• Rearrange the linear equation to make one variable the subject

• Then substitute this expression into the quadratic equation

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When giving your final answer for a quadratic simultaneous equations question, you must indicate clearly which x and y values go together.

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With quadratic simultaneous equations, if the resulting quadratic has no solutions after substitution, then on a graph showing both equations the line does not intersect with the curve.

With quadratic simultaneous equations, if the resulting quadratic has only one unique solution after substitution, it means that on a graph showing both equations the line only touches the curve at one point.