   SEARCH HOME Math Central Quandaries & Queries  Question from oreanna, a student: How do u solve 2x+9y=3 7x-4y=-25 in elimination Let me illustrate with a different pair of equations

2x - 3y = 4

and

5x + 4y = 10.

I am going to solve the problem and then explain why I chose the steps I did.

First multiply the first equation by 4 and the second equation by 3 to get

8x - 12y = 16

15x + 12y = 30.

Look at the coefficients of y in the two equations, one is 12 and the other is -12.

8x - 12y is 16 and 15x + 12y is 30 so (8x -12y) + (15x + 12y) is 16 + 30, that is

(8x -12y) + (15x + 12 y) = 16 + 30

or

23x = 46 and thus x = 2.

I hope now you can see why I wanted the coefficients of y in the two equations to be 12 and -12. When I added the two equations the y-term was "eliminated". To complete the problem substitute x = 2 into either of the two original equations and solve for y.

Before you go back to your problem look at mine again

2x - 3y = 4

and

5x + 4y = 10.

I chose to eliminate y but I could have eliminated x. To do so multiply the first equation by -5 and the second by 2 and add the resulting equations. Check that you got the same answer that you obtained by eliminating y.

Now try your problem,
Penny      Math Central is supported by the University of Regina and the Imperial Oil Foundation.