# 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.