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 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 in 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**