SOLUTION: Can you please help me solve this linear equation using substitution 1/2x + 2/3y = 1 1/4x - 1/3y = 5/2 Thank you.

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Question 701519: Can you please help me solve this linear equation using substitution
1/2x + 2/3y = 1
1/4x - 1/3y = 5/2
Thank you.

Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
It's not perfectly clear to me, but
I assume that the problem is system%28%281%2F2%29x+%2B+%282%2F3%29y+=+1%2C%281%2F4%29x+-+%281%2F3%29y+=+5%2F2%29, and I'll solve that.

If I had a choice, I would not solve that system by substitution.
%281%2F4%29x+-+%281%2F3%29y+=+5%2F2+ --> %281%2F4%29x+=+%281%2F3%29y%2B5%2F2+ --> x=%284%2F3%29y%2B10
Substituting %284%2F3%29y%2B10 for x in %281%2F2%29x+%2B+%282%2F3%29y+=+1 we get
%281%2F2%29%28%284%2F3%29y%2B10%29+%2B+%282%2F3%29y+=+1 --> %282%2F3%29y%2B5%2B+%282%2F3%29y+=+1 --> %284%2F3%29y=1-5 --> %284%2F3%29y=-4 --> %283%2F4%29%284%2F3%29y=-4%283%2F4%29 --> highlight%28y=-3%29.
Then, substituting %28-3%29 for y in x=%284%2F3%29y%2B10, we get
x=%284%2F3%29%28-3%29%2B10 --> x=-4%2B10 --> highlight%28x=6%29.

If I could choose how to solve it,
I would first transform the equations,
so as to get equivalent equations without fractions.
%281%2F2%29x+%2B+%282%2F3%29y+=+1 --> 3x%2B4y=6 (multiplying everything times 6)
%281%2F4%29x+-+%281%2F3%29y+=+5%2F2+ --> 3x-4y=30 (multiplying everything times 12)
Then I would add both equations to get
6x=36 --> highlight%28x=6%29.
I would also subtract the second equation from the first one to get
8y=-24 --> highlight%28y=-3%29.

IF THE PROBLEM WAS
system%281%2F2x+%2B+2%2F3y+=+1%2C1%2F4x+-+1%2F3y+=+5%2F2+%29,
That's the same as
.
That could be solve the same way for 1%2Fx and 1%2Fy to get
1%2Fx=6 and 1%2Fy=-3
Then the solutions would be x=1%2F6 and y=-1%2F3.