SOLUTION: y=3x and x + y=2 answer: 1/2, 3/2 wanted to know how my book got these fractions as answer need full break down

Algebra ->  Systems-of-equations -> SOLUTION: y=3x and x + y=2 answer: 1/2, 3/2 wanted to know how my book got these fractions as answer need full break down       Log On


   



Question 186409: y=3x and x + y=2

answer: 1/2, 3/2
wanted to know how my book got these fractions as answer need full break down

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
(1) y+=+3x and
(2) x+%2B+y+=+2
There are 2 equations and 2 unknowns. Whenever the
number of unknowns matches the number of equations,
then a solution is possible.
First, subtract y from both sides of (1)
(1) y+=+3x
(1) 0+=+3x+-+y
Now simply add (1) and (2)
(1) 3x+-+y+=+0
(2) x+%2B+y+=+2
(3) 4x+=+2
(3) x+=+1%2F2
To find y, substitute x+=+1%2F2 in (1)
(1) y+=+3x
(1) y+=+3%2A%281%2F2%29
(1) y+=+3%2F2
The solution is x+=+1%2F2 and y+=+3%2F2