SOLUTION: How do I solve this system using elimination? In steps please. 6/x-3/y=-4 and 9/x+9/y=21

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Question 930458: How do I solve this system using elimination? In steps please.
6/x-3/y=-4 and 9/x+9/y=21
Found 3 solutions by Alan3354, TimothyLamb, MathTherapy:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
How do I solve this system using elimination? In steps please.
6/x-3/y=-4 and 9/x+9/y=21
---
Sub for 1/x and 1/y, r & s will work
6r - 3s = -4
3r + 3s = 7 (divided by 3)
------------------------------- Add
Then sub back.

Answer by TimothyLamb(4379) About Me  (Show Source):
You can put this solution on YOUR website!
6/x - 3/y = -4
9/x + 9/y = 21
---
6y/xy - 3x/xy = -4
6y - 3x = -4xy
---
9/x + 9/y = 21
9y/xy + 9x/xy = 21
9y + 9x = 21xy
---
6y - 3x = -4xy
9y + 9x = 21xy
---
21(6y - 3x = -4xy)
4(9y + 9x = 21xy)
---
21*6y - 21*3x = -21*4xy
4*9y + 4*9x = 4*21xy
---
add the two equations:
---
21*6y + 4*9y - 21*3x + 4*9x = 0
(21*6 + 4*9)y - (21*3 + 4*9)x = 0
162y - 99x = 0
162y = 99x
---
answer:
y = (99/162)x
---
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Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

How do I solve this system using elimination? In steps please.
6/x-3/y=-4 and 9/x+9/y=21
Let x+=+1%2Fa, and y+=+1%2Fb

Then:

6%2Fx+-+3%2Fy+=+-+4 becomes: 6a – 3b = - 4 ------- eq (i)

9%2Fx+%2B+9%2Fy+=+21 becomes: 9a + 9b = 21_____3(3a + 3b) = 3(7)_____3a + 3b = 7 ---------- eq (ii)

9a = 3 --------- Adding eqs (ii) &(i)

a+=+3%2F9, or 1%2F3



6%281%2F3%29+-+3b+=+-+4 --------- Substituting 1/3 for a in eq (i)

2 – 3b =  – 4 

– 3b = – 4 – 2 

– 3b =  – 6

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



Since a+=+1%2F3, then 1%2Fa+=+1%2F%281%2F3%29, or 3

Now, since x+=+1%2Fa+=+3, then highlight_green%28x+=+3%29



Since b = 2, then 1%2Fb+=+1%2F2

Now, since y+=+1%2Fb+=+1%2F2, then highlight_green%28y+=+1%2F2%29

You can do the check!! 

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