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Question 1031509: Solve by substitution:
3x+5y=16
5x-7y=-4
I know the answer is (2,2), because I can solve this by the addition method by multiplying each by the coefficients of x, and solve. Easy Peasy!
But when I try the substitution method, it all goes straight to huge fractions that don't reduce to 2, by any means. I read this as, take the 1st equation and solve for y, and substitute the y value in the second and solve.
I am messing up somewhere, please help:) and Thanks!
Answer by fractalier(6550)   (Show Source):
You can put this solution on YOUR website! Yes, you have the right idea, and yes, working a problem like this via substitution is the hard way...but here goes...doing it as you recommend...
3x+5y=16
5y = -3x + 16
y = (-3/5)x + 16/5
Now substitute this into the second equation and get
5x - 7((-3/5)x + 16/5) = -4
5x + (21/5)x - 112/5 = -4
Multiply everything by 5 and get
25x + 21x - 112 = -20
46x - 112 = -20
46x = 92
x = 2
Now plug back in to the first one and get
3(2) + 5y = 16
6 + 5y = 16
5y = 10
y = 2
There you are...(2,2)
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