 #### Revision Notes

##### What are linear simultaneous equations?

When there are two unknowns (say x and y) in a problem, we need two equations to be able to find them both. These are called Simultaneous Equations.

If they just have x and y in them (no x2 or y2) then they are Linear Simultaneous Equations. (They can be represented by two straight lines on a graph – the two answers are the x and y coordinates of the point of intersection of the lines.)

##### How do you solve linear simultaneous equations?

The method described here is called the Elimination (or Balance) Method:

Label the equations A and B

1. Multiply A and/or B by numbers to make the coefficients of x or y the same size.
2. Add or subtract appropriate equations to eliminate that variable.

(Note: if the coefficients you made the same size in 1. have different signs you will be adding.  If they have the same signs you will be subtracting.)

1. Solve the resulting equation.
2. Substitute back into A or B and solve to find the other variable.
3. Check your answer by substituting into the equation you didn’t use in 4.

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