SOLUTION: Solve for x & y. 2/x-3/y=-5 4/x+6/y=14 Thanks for your help.

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Question 936776: Solve for x & y. 2/x-3/y=-5 4/x+6/y=14 Thanks for your help.
Found 2 solutions by MathLover1, MathTherapy:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
2%2Fx-3%2Fy=-5
4%2Fx%2B6%2Fy=14
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2y%2Fxy-3x%2Fxy=-5
4y%2Fxy%2B6x%2Fxy=14
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%282y-3x%29%2Fxy=-5
%284y%2B6x%29%2Fxy=14
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2y-3x=-5xy
4y%2B6x=14xy
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2y-3x%2B5xy=0 ...all terms multiply by 2
4y%2B6x-14xy=0
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4y-6x%2B10xy=0
4y%2B6x-14xy=0
_____________________add
4y-cross%286x%29%2B10xy%2B4y%2Bcross%286x%29-14xy=0
8y-4xy=0
4y%282-x%29=0
solutions:
find x
if 2-x=0=>highlight%28x=2%29
go to 2%2Fx-3%2Fy=-5 plug in 2 for x and find y
2%2F2-3%2Fy=-5
1-3%2Fy=-5
1%2B5=3%2Fy
6=3%2Fy
6y=3
y=3%2F6
highlight%28y=1%2F2%29

check:
2%2F2-3%2F%281%2F2%29=-5 =>1-6=-5
4%2F2%2B6%2F%281%2F2%29=14=>2%2B12=14


Answer by MathTherapy(10551) About Me  (Show Source):
You can put this solution on YOUR website!
Solve for x & y. 2/x-3/y=-5 4/x+6/y=14 Thanks for your help.


2%2Fx+-+3%2Fy+=+-+5 ------- eq (i)

4%2Fx+%2B+6%2Fy+=+14 ------- eq (ii)

Let a+=+1%2Fx, and b+=+1%2Fy

Then 2%2Fx+-+3%2Fy+=+-+5 becomes: 2a – 3b = - 5 ------ eq (iii)

Also, 4%2Fx+%2B+6%2Fy+=+14 becomes: 4a + 6b = 14 ------- eq (iv)

4a – 6b = - 10 -------- Multiplying eq (iii) by 2 ----- eq (v)

8a = 4 ------- Adding eqs (v) & (iv)

a = 4%2F8, or 1%2F2 



2%281%2F2%29+-+3b+=+-+5 -------- Substituting ½ for a in eq (iii) 

1 – 3b = - 5 

– 3b = - 5 – 1 

– 3b = - 6

b = %28-+6%29%2F%28-+3%29, or 2



Since system%28a+=+%281%2F2%29_and%2Ca+=+1%2Fx%29, then 1%2F2+=+1%2Fx

x+=+2 ------ Cross-multiplying



Since system%28b+=+2_and%2Cb+=+1%2Fy%29, then 2+=+1%2Fy

2y = 1 ------ Cross-multiplying

y+=+1%2F2



highlight_green%28system%28x+=+2_and%2Cy+=+1%2F2%29%29