Simultaneous equations involve two variables, the values of which need to be found.

 

The following method quickly eliminates one of the variables, so that the resulting equation can be solved normally.

 

Example

Solve simultaneously:

x + y = 6

2x - 3y = 2

 

Answer

x + y = 6     (a)

2x - 3y = 2      (b)

 

In order to eliminate, we must have matching coefficients.

Multiply (a) by 3 so that we can eliminate the y terms.

 

 

3x + 3y = 18     (a)

2x - 3y = 2      (b)

 

We can eliminate y by adding (a) to (b)

This gives 5x = 20

So x = 4

 

Substitute this x value into one of the equations, say (a) to get

4 + y = 6

y = 2

 

Check by putting this into the other equation (b) to get 2 x 4 - 3 x 2 = 8 - 6 = 2

 

Solution is x = 4, y = 2

 

This looks tricky, but you'll soon get to grips with it if you work through it one step at a time, and write everything down!