SOLUTION: elimination method 2x/3 + 3y/4 =11/12 x/3 + 7y/18 =1/2 wouldn't 12 be the common denominator in the first equation help

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Question 44653: elimination method
2x/3 + 3y/4 =11/12
x/3 + 7y/18 =1/2
wouldn't 12 be the common denominator in the first equation
help
Found 2 solutions by adamchapman, venugopalramana:
Answer by adamchapman(301) About Me  (Show Source):
You can put this solution on YOUR website!
You are right about 12 being the common denominator for the first equation.
My working is shown below. Hopefully this example will help you in future questions of this type:
2x%2F3+%2B+3y%2F4+=11%2F12
8x%2F12+%2B+9y%2F12+=11%2F12
Rearrange to give y in terms of x:
9y%2F12+=%2811-8x%29%2F12
9y+=%2811-8x%29
y+=%2811-8x%29%2F9 ......................(1)
Now the second part:
x%2F3+%2B+7y%2F18+=1%2F2+.............................(2)
Substituite equation (1) into equation (2) for y:
x%2F3+%2B+7%2811-8x%29%2F%2818%2A9%29+=1%2F2
x%2F3+%2B+%2877-56x%29%2F%28162%29+=1%2F2
Rearrange to give x:
x%2F3%2B77%2F162-56%2F162=1%2F2
Rearrange to give x:
x%2F3%2B21%2F162=1%2F2
x%2F3=1%2F2-21%2F162
x%2F3=81%2F162-21%2F162
x%2F3=60%2F162
x=180%2F162
x=10%2F9.................................(3)
Substitute equation (3) into equation (1) to find y:
y+=%2811-8%2810%2F9%29%29%2F9
y+=%2811-80%2F9%29%2F9
y=19%2F81
So the solution to the two original equations is x=10/9 and y=19/81.
I hope this helps.
P.S. I am trying to start up my own homework help website. I would be extremely grateful if you would e-mail me some feedback on the help you received to adam.chapman@student.manchester.ac.uk
Adam







Answer by venugopalramana(3286) About Me  (Show Source):
You can put this solution on YOUR website!
elimination method
2x/3 + 3y/4 =11/12..........I
x/3 + 7y/18 =1/2..........II
wouldn't 12 be the common denominator in the first equation
YES SO MULTIPLY WITH 12...EQN.I
8X+9Y=11...............III
SIMILARLY MULTIPLY EQN.II WITH 18
6X+7Y=9..............IV
7*EQNIII-9*EQN.IV
56X+63Y-72X-63Y=77-81
-16X=-4
X=1/4...PUT IN EQN.III
8*1/4+9Y=11
9Y=11-2=9
Y=1