Question

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

Answer 1

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!