## Simultaneous Equations: Substitution Method

This is exactly the same method we use to find where two lines intersect.

Process:

- Rearrange one of the equations to make one of the variables a subject
- Substitute for this variable into the other equation
- Solve the resulting equation
- Substitute these solutions into one of the original equations to find the values of the other variable

Example

Solve the system of equations

Substitute eqn 1 into eqn 2

Substituting into eqn 1 gives

Solve the system of equations

Rearrange eqn 2 to make y the subject

Substitute eqn 3 into eqn 1

Factorising gives

Substituting these values into eqn 3 gives

So the solutions are

Solve the system of equations

Rearranging eqn 2 to make y the subject gives

Substituting eqn 3 into eqn 1 gives

Substituting the value of x into eqn 3 gives

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Categories: Equations

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