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3/4x - 1/3y = 2 and 1/2x + 2/3 y = 4

Guest Apr 23, 2017
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 #1
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Solve the following system:
{(3 x)/4 - y/3 = 2 | (equation 1)
x/2 + (2 y)/3 = 4 | (equation 2)

Subtract 2/3 × (equation 1) from equation 2:
{(3 x)/4 - y/3 = 2 | (equation 1)
0 x+(8 y)/9 = 8/3 | (equation 2)

Multiply equation 1 by 12:
{9 x - 4 y = 24 | (equation 1)
0 x+(8 y)/9 = 8/3 | (equation 2)
Multiply equation 2 by 9/8:

{9 x - 4 y = 24 | (equation 1)
0 x+y = 3 | (equation 2)

Add 4 × (equation 2) to equation 1:
{9 x+0 y = 36 | (equation 1)
0 x+y = 3 | (equation 2)

Divide equation 1 by 9:
{x+0 y = 4 | (equation 1)
0 x+y = 3 | (equation 2)

Collect results:
Answer: | x = 4      and          y = 3

Guest Apr 23, 2017
 #2
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3/4x - 1/3y = 2 and 1/2x + 2/3 y = 4

 

\(\frac{3}{4}x-\frac{1}{3}y=2\\\frac{1}{2}x+\frac{2}{3}y=4\) 

 

\(\frac{6}{4}x-\frac{2}{3}y=4\)

 

\(\frac{6}{4}x-4=\frac{2}{3}y\\4-\frac{1}{2}x=\frac{2}{3}y\)

 

\(\frac{6}{4}x-4=4-\frac{1}{2}x\\\frac{6}{4}x+\frac{2}{4}x=8\\2x=8\)

 

\(x=4\)

 

\(\frac{1}{3}y=\frac{3}{4}x-2\\y=\frac{9}{4}x-6=\frac{9}{4}\cdot 4-6\)

 

\(y=3\)

 

laugh  !

asinus  Apr 23, 2017
edited by asinus  Apr 23, 2017

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