SOLUTION: Hi! Please help me, I'm stuck 1/2x + 1/3y = 13 2/5x + 1/4y =10

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Question 154839: Hi! Please help me, I'm stuck
1/2x + 1/3y = 13
2/5x + 1/4y =10

Found 2 solutions by Fombitz, checkley77:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
1.%281%2F2%29x+%2B+%281%2F3%29y+=+13
2.%282%2F5%29x+%2B+%281%2F4%29y+=10
First step I use when dealing with fractions is to multiply to get rid of all denominators.
Multiply all equations by 3*4*5=60.
1.30x%2B20y=780
2.24x%2B15y=600
Multiply eq. 1 by 4 and eq. 2 by -5 and add them.
This will get rid of x.
1.120x%2B80y=3120
2.-120x-75y=-3000
%28120x%2B80y%29%2B%28-120x-75y%29=3120-3000
5y=120
highlight%28y=24%29
Use either eq. 1 or 2 to solve for y.
1.30x%2B20y=780
30x%2B20%2824%29=780
30x%2B480=780
30x=300
highlight%28x=10%29

Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
1/2x + 1/3y = 13 MULTIPLY THIS EQUATION BY 1/4.
2/5x + 1/4y =10 MULTIPLY THIS EQUATION BY -1/3 & ADD.
1/2X*1/4+1/3Y*1/4=13*1/4
2/5X*-1/3+1/4Y*-1/3=10*-1/3
----------------------------------
1/8X-2/15X+1/12Y-1/12Y=13/4-10/3
X/8+2X/15=(13*3+4*10)/4*3
(15X+8*2X)/120=(39-40)/12
(15X-16X)/120=-1/12
-X/120=-1/12
-12X=-120
X=-120/-12
X=10 ANSWER.
1/2*10+Y/3=13
5+Y/3=13
Y/3=13-5
Y/3=8
Y=24 ANSWER.
PROOF:
2/5*10+1/3*24=10
4+6=10
10=10