Solve 0.3x - 0.y = 4, 0.2x + 0.3y = -37/17 by elimination

[dsj1023]

I am trying to solve this problem using the elimination method when the answer is a fraction

.3x - .2y = 4
.2x + .3y = -37/17

I took the top equation times 3 and the bottom equation times 2 so that the y's would subtract out. That left me with:
1.3x = 7 11/17

From there everything got messy and I got lost. This is my first time posting a problem on here so if I didn't do something right in posting please let me know!

[galactus]

First, shed the decimals by multiplying by 10:

3x-2y=40
2x+3y=\frac{-370}{17}

Multiply the first row by 2 and the second row by -3:

6x-4y=80
-6x-9y=\frac{1110}{17}

Now, add them and get rid of the x value:

-13y=\frac{2470}{17}

There's a start.

[dsj1023]

OK I took your start and here's what I did:

6x - 4y = 80
-6x - 9y = 1110/17

-13y = 2470/17

y = -11 39/221

3x - (2)-1139/221 = 40
3x - (-22 78/221) = 40
3x + 22 78/221 = 40
3x = -62 78/221
x = -20 520/663

Am I way off base here? Thanks for replying as quickly as you did!

[galactus]

Please, try not use mixed numbers. Keep them in improper fraction form.

Try y again. Shouldn't that be y= -190/17. Or, if you must, 11 3/17

[dsj1023]

I keep getting the same thing for y - I'm not coming up with the answer you got.

[galactus]

-13y=\frac{2470}{17}

y=\frac{-2470}{221}=\frac{-190}{17}

[dsj1023]

OK I figured it out - so x then equals 100/17.
Thanks!