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

1 Answer
Feb 22, 2016

Isolate x in the second equation.

Explanation:

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

Solve by completing the square.

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!