Solving 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

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