Question 1175906
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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.



<pre>
    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.


<U>ANSWER</U>.  There are two solutions:  a) x=2,  y= -3   and   b) x= -1, y= 6.
</pre>

Solved.