Simultaneous Equations (Cambridge (CIE) IGCSE Maths)

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

E.g. and .

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

E.g. For the pair of simultaneous equations and :

1. Multiply one equation to make the coefficient of one variable the same, Multiply by to get .

2. Add or subtract the equations to eliminate a variable,

3. Solve to find one variable, .

4. Substitute into one of the equations and solve for the other variable, .

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.

E.g. For the pair of simultaneous equations and :

1. Rearrange the first equation to make the subject, .

2. Then substitute the expression for into the second equation, .

3. Solve for , .

4. Substitute the value for into one of the equations and solve for , .

To solve linear simultaneous equations using a graph, plot both equations on the same set of axes and find the point of intersection.

The - and - coordinates of that point give the solutions for and .

True.

It is a good idea to 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 ( or or ).

To use substitution to solve quadratic simultaneous equations:

• Rearrange the linear equation to make one variable the subject.

• Substitute this expression into the quadratic equation.

True.

When giving your final answer for a quadratic simultaneous equations question, there will typically be two pairs of solutions.

You must indicate clearly which and values go together.

True.

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.