Solve L_{2}:2x+3y+3=0

$$L _ { 2 } : 2 x + 3 y + 3 = 0$$

Solve for L_2 (complex solution)

$$\left\{\begin{matrix}L_{2}=-\frac{6\left(y+1\right)}{x}\text{, }&x\neq 0\\L_{2}\in \mathrm{C}\text{, }&y=-1\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2.

$$L_{2}x+6y+6=0$$

Subtract 6y from both sides. Anything subtracted from zero gives its negation.

$$L_{2}x+6=-6y$$

Subtract 6 from both sides.

$$L_{2}x=-6y-6$$

The equation is in standard form.

$$xL_{2}=-6y-6$$

Divide both sides by x.

$$\frac{xL_{2}}{x}=\frac{-6y-6}{x}$$

Dividing by x undoes the multiplication by x.

$$L_{2}=\frac{-6y-6}{x}$$

Divide -6y-6 by x.

$$L_{2}=-\frac{6\left(y+1\right)}{x}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=-\frac{6\left(y+1\right)}{L_{2}}\text{, }&L_{2}\neq 0\\x\in \mathrm{C}\text{, }&y=-1\text{ and }L_{2}=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2.

$$L_{2}x+6y+6=0$$

Subtract 6y from both sides. Anything subtracted from zero gives its negation.

$$L_{2}x+6=-6y$$

Subtract 6 from both sides.

$$L_{2}x=-6y-6$$

Divide both sides by L_{2}.

$$\frac{L_{2}x}{L_{2}}=\frac{-6y-6}{L_{2}}$$

Dividing by L_{2} undoes the multiplication by L_{2}.

$$x=\frac{-6y-6}{L_{2}}$$

Divide -6y-6 by L_{2}.

$$x=-\frac{6\left(y+1\right)}{L_{2}}$$

Solve for L_2

$$\left\{\begin{matrix}L_{2}=-\frac{6\left(y+1\right)}{x}\text{, }&x\neq 0\\L_{2}\in \mathrm{R}\text{, }&y=-1\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2.

$$L_{2}x+6y+6=0$$

Subtract 6y from both sides. Anything subtracted from zero gives its negation.

$$L_{2}x+6=-6y$$

Subtract 6 from both sides.

$$L_{2}x=-6y-6$$

The equation is in standard form.

$$xL_{2}=-6y-6$$

Divide both sides by x.

$$\frac{xL_{2}}{x}=\frac{-6y-6}{x}$$

Dividing by x undoes the multiplication by x.

$$L_{2}=\frac{-6y-6}{x}$$

Divide -6y-6 by x.

$$L_{2}=-\frac{6\left(y+1\right)}{x}$$

Solve for x

$$\left\{\begin{matrix}x=-\frac{6\left(y+1\right)}{L_{2}}\text{, }&L_{2}\neq 0\\x\in \mathrm{R}\text{, }&y=-1\text{ and }L_{2}=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2.

$$L_{2}x+6y+6=0$$

Subtract 6y from both sides. Anything subtracted from zero gives its negation.

$$L_{2}x+6=-6y$$

Subtract 6 from both sides.

$$L_{2}x=-6y-6$$

Divide both sides by L_{2}.

$$\frac{L_{2}x}{L_{2}}=\frac{-6y-6}{L_{2}}$$

Dividing by L_{2} undoes the multiplication by L_{2}.

$$x=\frac{-6y-6}{L_{2}}$$

Divide -6y-6 by L_{2}.

$$x=-\frac{6\left(y+1\right)}{L_{2}}$$