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help needed!!!

 
 
gerd
 
Reply Fri 22 Sep, 2006 10:01 am
Hi friends, I need to solve this system:

5x + 40 = 64xy

2x - 40 = 20xy


could anyone explain me please step by step?

Thaks a lot Very Happy
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Type: Discussion • Score: 1 • Views: 719 • Replies: 4
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fresco
 
  1  
Reply Fri 22 Sep, 2006 11:13 am
Rewrite
5x+ 40 = 64xy
x - 20 = 10xy

Eliminate xy by finding LCM of 64and 10, multiplying each equation by LCM and subtracting. Hence solve for x then for y.
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Brandon9000
 
  1  
Reply Fri 22 Sep, 2006 11:58 am
Re: help needed!!!
gerd wrote:
Hi friends, I need to solve this system:

5x + 40 = 64xy

2x - 40 = 20xy


could anyone explain me please step by step?

Thaks a lot Very Happy


Lets simply add the two equations:

7x = 84xy

Assuming x is not zero (looking at the original equations, there is clearly no solution with x = 0), we can obtain the solution by dividing this equation by x:

7 = 84y

y = 1/12

Substituting this result back into 5x + 40 = 64xy, we obtain:

5x + 40 = (5 1/3) x

40 = (1/3)x

x = 120
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gerd
 
  1  
Reply Fri 22 Sep, 2006 12:41 pm
Thank you fresco and Brandon9000, you both were very helpful. Very Happy
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fresco
 
  1  
Reply Sat 23 Sep, 2006 05:08 am
Gerd,

Sorry, LCM doesnt come into it ! (Alzheimers ? Smile )

Multply first equation by 10 and second by 64 giving

50x + 400 = 64x - 1280

Whence x = 120

substituting

120 - 20 = 1200y
y = 1/12

which agrees with Brandon.
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