Solve 11x-2y-5=x^2-y

$$11x-2y-5= { x }^{ 2 } -y$$

Solve for y

$$y=-x^{2}+11x-5$$

Steps for Solving Linear Equation

Add y to both sides.

$$11x-2y-5+y=x^{2}$$

Combine -2y and y to get -y.

$$11x-y-5=x^{2}$$

Subtract 11x from both sides.

$$-y-5=x^{2}-11x$$

Add 5 to both sides.

$$-y=x^{2}-11x+5$$

Divide both sides by -1.

$$\frac{-y}{-1}=\frac{x^{2}-11x+5}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$y=\frac{x^{2}-11x+5}{-1}$$

Divide x^{2}-11x+5 by -1.

$$y=-\left(x^{2}-11x+5\right)$$

Solve for x (complex solution)

$$x=\frac{-\sqrt{101-4y}+11}{2}$$

$$x=\frac{\sqrt{101-4y}+11}{2}$$

Solve for x

$$x=\frac{-\sqrt{101-4y}+11}{2}$$

$$x=\frac{\sqrt{101-4y}+11}{2}\text{, }y\leq \frac{101}{4}$$