Given 4x+7y=25 and 2x+5y=17, identify x and y by solving the simultaneous equations

First thing we have to do is to eliminate one of the variables, either x or y (it doesn’t matter which one). In order to achieve that, we aim to have the same co-efficient (number in front of x or y) of a variable in both equations.

In this example, we can observe that no co-efficient is the same so we have to do some manipulation first before eliminating a variable!

Multiplying 2x+5y=17 by 2, give us 4x+10y=34 (Remember to multiply by 2 all the numbers)

Now that we have the same x co-efficient in both equations we can eliminate the x variable by subtracting one equation from the other:

    4x + 10y = 34

–  4x + 7y = 25

3y=9

 y=3

Hence, we can substitute y in one of the initial equations e.g. 2x+5y=17

2x+5(3) = 17

2x=17-15

2x=2

x=1

Therefore, the variables are x=1 and y=3