Simultaneous equations involve two variables, each of whose value must 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**