How do I solve a simultaneous equation?

You will be presented with two equations, both with two unknown values. For example:

8x-2y=19

and

3x=5+y

 

To begin, we are going to move both unknown terms in the second equation to the same side:

3x-y=5

 

Then, we are going to multiply this entire equation by 2, in order to have equal y values:

6x-2y=10

 

At this point, we will subtract the manipulated second equation to the first, so that we cancel out the y values:

2x=9

 

Now we can find the value of x by dividing by 2:

x=4.5

 

With this value of x, we can find the value of y through substitution. Putting our value for x into the first equation:

8(4.5)-2y=19

36-2y=19

36=19+2y

17=2y

8.5=y

 

Having shown this working, you can give the answer on your paper as follows:

x=4.5, y=8.5

 

Remember you will always need to show your working when doing this in an exam.