Solve x^2-5xy+1=3

$$x ^ { 2 } - 5 x y + 1 = 3$$

Solve for y

$$y=\frac{x}{5}-\frac{2}{5x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Subtract x^{2} from both sides.

$$-5xy+1=3-x^{2}$$

Subtract 1 from both sides.

$$-5xy=3-x^{2}-1$$

Subtract 1 from 3 to get 2.

$$-5xy=2-x^{2}$$

The equation is in standard form.

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

Divide both sides by -5x.

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

Dividing by -5x undoes the multiplication by -5x.

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

Divide 2-x^{2} by -5x.

$$y=\frac{x}{5}-\frac{2}{5x}$$

Solve for x

$$x=\frac{\sqrt{25y^{2}+8}+5y}{2}$$

$$x=\frac{-\sqrt{25y^{2}+8}+5y}{2}$$