+0  
 
0
310
2
avatar

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

Guest Apr 23, 2017
 #1
avatar
+1

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
avatar+7629 
+1

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

16 Online Users

avatar
avatar
avatar

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.