SOLUTION: Hello. I'm trying to solve the following system, but I keep running into fractions rather than whole numbers. (1) If I get rid of the fractions on the first equation by multiplyi

Question 79277: Hello. I'm trying to solve the following system, but I keep running into fractions rather than whole numbers. (1) If I get rid of the fractions on the first equation by multiplying it by 8, then again by 12... and (2) multiply the second equation by 10 to eliminate Y, I get X = 1644/38 or 4.2590.
On the other hand, if I try by susbstitution (Y=5x/12 - 252) from the second equation into the first one, I get X = 79.33.
(7/2)X + (5/4)Y = 4
(5/6)X - 2Y = 21
What am I doing wrong? Shouldn't I get a whole number for an answer? Please help. Thanks for your generosity.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
(7/2)X + (5/4)Y = 4
(5/6)X - 2Y = 21
--------------------
Multiply thru 1st be 8 and 2nd by 6 to get:
---------
28x + 10y = 32
5x - 12y = 126
--------------------
Divide thru 1st be 2 to get:
14x + 5y = 16
5x - 12y = 126
--------------------
Multiply 1st by 5 and 2nd by 14 so you can get rid of the x terms:
70x + 25y = 80
70x - 168y = 1764
--------------
Subtract 1st from 2nd to get:
-193y = 1684
y = -8.7254
--------
Go back two steps:
Multiply 1st by 12 and 2nd by 5 to get rid of the y terms:
----------
168x + 60y = 192
25x - 60y = 630
----------
Add to get rid of the y-terms and to solve for "x":
193x = 822
x= 4.2591
==================
Cheers,
Stan H.
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