Solve for x and y? xy-x^2= -20 x-2y=3

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Answer 1 · 2016-02-22T22:40:48

Isolate x in the second equation.

#x - 2y = 3#

#x = 3 + 2y#

Now, solve by substitution. This can be done by substituting that equation in the place of x in the other equation.

#(3 + 2y)y - (3 + 2y)^2 = -20#

#3y + 2y^2 - (9 + 4y^2 + 12y) = -20#

#3y + 2y^2 - 9 - 4y^2 - 12y = -20#

#2y^2 - 9y + 11 = 0#

#2(y^2 - 9/2y) = -11#

#2(y^2 - 9/2y+ m) = -11#

#m = (b/2)^2#

#m = ((-9/2)/2)^2#

#m = 81/16#

#2(y^2 - 9/2y + 81/16) = -11#

#2(y - 9/4)^2 = -11#

#(y - 9/4)^2 = -11/2#

#(y - 9/4) = sqrt(-11/2)#

Since the square root of a negative number is not defined, the equation has no real solutions. The solution set is #{O/}#.

Hopefully this helps!