System of two equations with fractions

1. May 23, 2013

Hivoyer

1. The problem statement, all variables and given/known data

These are the two equations:

(7 + x)/5 - (2x - y)/4 - 3y = -5
(5y - 7)/2 - (4x - 3)/6 - 18 = -5x

2. Relevant equations

3. The attempt at a solution

When I try to simplify it, I end up with:

6x + 55y = 128
34x + 15y = 129

I'm not sure where to go with this, I think I should have gone a different route instead of just trying to simplify the equations.Does anyone know where I might have gone wrong?
By the way, in the answers of the book it says that X is 3 and Y is 2, however I must find them by solving the problem, but I am stuck.Any help would be appreciated.

2. May 23, 2013

haruspex

Are you sure you've stated the problem correctly? The second one is perhaps = -6x on the right?
Have you not been shown how to solve simultaneous equations? It's very easy. One way is to write one of the equations in the form y = (some expression with x and constants but no y's), then use that to replace y in the other equation.

3. May 23, 2013

Hivoyer

Yeah thanks, but it seems like the problem is wrong, the second equation doesn't add up with the answer they've given, even when I calculate it with software.

4. May 23, 2013

Ray Vickson

The solution of your two equations (exactly as written) is x = 501/134, y = 643/335. Are you sure you wrote the correct equations?

BTW: when I (or, actually, Maple 14) simplify your equations I get
$$6x + 55y = 128\\ 26x + 15y = 126$$
and these also give the values of x and y as stated above.

5. May 23, 2013

SteamKing

Staff Emeritus
Check your arithmetic on both equations.