SOLUTION: 4x + y = 3 1/2 x2 - 4xy = 3 Find x and y

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Question 1208473: 4x + y = 3 1/2
x2 - 4xy = 3
Find x and y
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


4x%2By=7%2F2
x%5E2-4xy=3 --> x%28x-4y%29=3

The first equation contains variable y by itself, so the best algebraic approach to solving the problem is solving the first equation for y and substituting in the second equation.

y=-4x%2B7%2F2

x%28x-4%28-4x%2B7%2F2%29%29=3
x%28x%2B16x-14%29=3
x%2817x-14%29=3
17x%5E2-14x=3
17x%5E2-14x-3=0
%2817x%2B3%29%28x-1%29=0

x=-3/17 or x=1

x=1 --> y=-4(1)+7/2=-1/2
First solution: (x,y) = (1,-1/2)

x=-3/17 --> y=-4(-3/17)+7/2=12/17+7/2=24/34+119/34=143/34
Second solution: (x,y) = (-3/17,143/34)

You can confirm the solutions using an online graphing utility like geogebra (geogebra.org).