Solve x^2+7xy+y=0

$${ x }^{ 2 } +7xy+y = 0$$

Solve for y

$$y=-\frac{x^{2}}{7x+1}$$

$$x\neq -\frac{1}{7}$$

Steps for Solving Linear Equation

Subtract x^{2} from both sides. Anything subtracted from zero gives its negation.

$$7xy+y=-x^{2}$$

Combine all terms containing y.

$$\left(7x+1\right)y=-x^{2}$$

Divide both sides by 7x+1.

$$\frac{\left(7x+1\right)y}{7x+1}=-\frac{x^{2}}{7x+1}$$

Dividing by 7x+1 undoes the multiplication by 7x+1.

$$y=-\frac{x^{2}}{7x+1}$$

Solve for x (complex solution)

$$x=\frac{\sqrt{y\left(49y-4\right)}-7y}{2}$$

$$x=\frac{-\sqrt{y\left(49y-4\right)}-7y}{2}$$

Solve for x

$$x=\frac{\sqrt{y\left(49y-4\right)}-7y}{2}$$

$$x=\frac{-\sqrt{y\left(49y-4\right)}-7y}{2}\text{, }y\geq \frac{4}{49}\text{ or }y\leq 0$$