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 1**

Solve simultaneously:

x + y = 4

x - y = 2

**Answer**

x + y = 4 (a)

x - y = 2 (b)

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

This gives 2x = 6

So x = 3

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

3 + y = 4

y = 1

Check by putting this into the other equation (b) to get 3 - 1 = 2

Solution is **x = 3, y = 1**

**Example 2**

Solve simultaneously:

3x + y = 25

x + y = 11

**Answer**

3x + y = 25 (a)

x + y = 11 (b)

We can eliminate y by subtracting (b) from (a) to get

2x = 14

x = 7

Substitute this x value into say equation (b) to get 7 + y = 11

So y = 4

Check in equation (a) to get 3 x 7 + 4 = 21 + 4 = 25

Solution is **x = 7, y = 4**

These may look tricky but the key is to take them slowly, one step at a time - and write everything down!