Elimination

If you are given a problem in which there are 2 variables and 2 equations, you can solve it through elimination. If for example you are given:

10x+6y=46 and 5x-2y=18

It would be very effective to use substitution in this case. With elimination, you are looking to "eliminate" one of the variables. So in this case, we look to see which variable would be easier eliminate, and it happens to be y.

If we look at all of the variables on one side of the equation and the answers on the other, we can eliminate y by multiplying all of the parts of the second equation by 3.

10x+6y=46

5x-2y=18

10x+6y=46

3(5x)3(-2y)=3(18)

and you end up with...

10x+6y=46

15x-6y=54

Now because we have all of the variables on one side, we can add the equations and have both 6y and -6y cancel each other out. Remember that when canceling variables out, they must have opposite signs. If opposite signs are not given, then you must multiply one of the equations by (-1) to get a negative sign and thus be able to add the equations.

what is left is:

10x+15x=46+54

We can combine the two terms on the left and the two terms on the right and we end up with:

25x=100

We then know that x=4, and we can plug that into either of the original equations to find the value of y.

10x+6y=46 ----> 10(4)+6y=46 ----> 40+6y=46 ----> 6y=6----> y= 1