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Question 1175906: Please help me solve 3x + y=3
xy =-6
Found 3 solutions by josgarithmetic, MathTherapy, ikleyn:
Answer by josgarithmetic(39617)   (Show Source):
Answer by MathTherapy(10552)  (Show Source):
Answer by ikleyn(52781)  (Show Source):
You can put this solution on YOUR website! .
Please help me solve 3x + y=3
xy =-6
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The setup in the post by @josgarithmetic is INCORRECT, so ignore his post.
I came to bring a correct solution.
3x + y = 3 (1)
xy = -6 (2)
From equation (1), express y = 3 - 3x = 3*(1-x) and substitute it into equation (2). You will get
3x*(1-x) = -6.
Simplify it step by step, making equivalent transformations
x*(1-x) = -2
x*(x-1) = 2
x^2 - x - 2 = 0
Factor left side
(x-2)*(x+1) = 0
The roots are x= 2 and x= -1.
To get y, consider these two cases separately.
a) If x = 2, then y = 3*(1-x) = 3*(1-2) = 3*(-1) = -3.
b) If x= -1, then y = 3*(1-x) = 3*(1-(-1)) = 3*2 = 6.
ANSWER. There are two solutions: a) x=2, y= -3 and b) x= -1, y= 6.
Solved.
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