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Question 5680: Here's the question: Sorry for it being so long
Solve each system by the addition method
x/3 - y/2 = -5/6
x/5 - y/3 = -3/5
This is what I did:
6*x/3 - 6*y/2 = 6*-5/6
2x - 3y = -5
15*x/3 - 15*y/3 = 15*-3/5
3x - 5y = -9
-3(2x - 3y) = -3*-5
-6x + 9y = 15
2(3x - 5y) = 2*-9
6x - 10y = -18
-6x + 9y = 15
6x - 10y = -18
-1y = -3
y = 3
for the first eq I substituted 3 for y to find x
x/3 - 3/2 = -56
6*x/3 - 6*3/2 = 6*-5/6
2x - 9 + 9 = -5 + 9
2x = 4
x = 2
TO TEST:
2/3 - 3/2 = -5/6
6*2/3 - 6*3/2 = 6*-5/6
4/3 - 9/2 = -5/6 (do you just subtract 9 from 4 and multiply the two denominators to get 6?)
(this is where I get stuck. Or is this how to test?)
2/5 - 1 = -3/5
(2/5 - 1/1 = -3/5)
(I think this tests right. I hope)
I can't figure out how to test this. I think I got the right answers for x and y, but I can't figure out how to test to see if they are correct. I tried, but it's not working out. I must be missing a step somewhere. Please help! Thank you. Maybe I got it right and am looking for something that isn't there. Algebra. ARGHHHHHHHHHH!
Answer by lotanez(23)   (Show Source):
You can put this solution on YOUR website! 1/3x - 1/2y = -5/6
1/5x - 1/3y = -3/5
First solve for x by using the first equation:
1/3x - 1/2y + 1/2y = -5/6 + 1/2y
1/3x = 1/2y - 5/6
1/3x/1/3 = 1/2y - 5/6 / 1/3
x = (1/2y - 5/6)3................. (-5/6)(3/1) = -15/6 = -5/2
x = 3/2y - 5/2
1/5x - 1/3y = -3/5
1/5(3/2y - 5/2) - 1/3y = -3/5
3/10y - 1/2 - 1/3y =-3/5....3/10y-1/3y=(3)3/10(3)-(10)1/3(10)=9/30-10/30=-1/30y
-1/30y - 1/2 + 1/2 = -3/5 + 1/2
-1/30y = -1/10
-1/30y/-1/30 = -1/10/-1/30
y = (-1/10)-30
y = 3
1/3x - 1/2y = -5/6
1/3x - 1/2(3) = -5/6
1/3x - 3/2 + 3/2 = -5/6 + 3/2
1/3x = 2/3
1/3x/1/3 = 2/3/1/3
x = (2/3)3
x = 2
To Check:
1/3(2) - 1/2(3) = -5/6
2/3 - 3/2 = -5/6
-5/6 = -5/6
Don't get frustrated, you'll get it. Hope this helps.
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