Math CentralQuandaries & 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


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


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


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,

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