Solving Simple Simultaneous Equations

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