Solve y(j2-2)-xj(j4+3)=2

$$y ( j 2 - 2 ) - x j ( j 4 + 3 ) = 2$$

Solve for j (complex solution)

$$\left\{\begin{matrix}j=\frac{j_{2}y-2y-2}{x\left(j_{4}+3\right)}\text{, }&j_{4}\neq -3\text{ and }x\neq 0\\j\in \mathrm{C}\text{, }&y=\frac{2}{j_{2}-2}\text{ and }j_{2}\neq 2\text{ and }\left(j_{4}=-3\text{ or }x=0\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply y by j_{2}-2.

$$yj_{2}-2y-xj\left(j_{4}+3\right)=2$$

Use the distributive property to multiply xj by j_{4}+3.

$$yj_{2}-2y-\left(xjj_{4}+3xj\right)=2$$

To find the opposite of xjj_{4}+3xj, find the opposite of each term.

$$yj_{2}-2y-xjj_{4}-3xj=2$$

Subtract yj_{2} from both sides.

$$-2y-xjj_{4}-3xj=2-yj_{2}$$

Add 2y to both sides.

$$-xjj_{4}-3xj=2-yj_{2}+2y$$

Combine all terms containing j.

$$\left(-xj_{4}-3x\right)j=2-yj_{2}+2y$$

The equation is in standard form.

$$\left(-j_{4}x-3x\right)j=2+2y-j_{2}y$$

Divide both sides by -j_{4}x-3x.

$$\frac{\left(-j_{4}x-3x\right)j}{-j_{4}x-3x}=\frac{2+2y-j_{2}y}{-j_{4}x-3x}$$

Dividing by -j_{4}x-3x undoes the multiplication by -j_{4}x-3x.

$$j=\frac{2+2y-j_{2}y}{-j_{4}x-3x}$$

Divide -yj_{2}+2y+2 by -j_{4}x-3x.

$$j=-\frac{2+2y-j_{2}y}{x\left(j_{4}+3\right)}$$

Solve for j_2 (complex solution)

$$\left\{\begin{matrix}j_{2}=\frac{jj_{4}x+3jx+2y+2}{y}\text{, }&y\neq 0\\j_{2}\in \mathrm{C}\text{, }&x=-\frac{2}{j\left(j_{4}+3\right)}\text{ and }j_{4}\neq -3\text{ and }j\neq 0\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply y by j_{2}-2.

$$yj_{2}-2y-xj\left(j_{4}+3\right)=2$$

Use the distributive property to multiply xj by j_{4}+3.

$$yj_{2}-2y-\left(xjj_{4}+3xj\right)=2$$

To find the opposite of xjj_{4}+3xj, find the opposite of each term.

$$yj_{2}-2y-xjj_{4}-3xj=2$$

Add 2y to both sides.

$$yj_{2}-xjj_{4}-3xj=2+2y$$

Add xjj_{4} to both sides.

$$yj_{2}-3xj=2+2y+xjj_{4}$$

Add 3xj to both sides.

$$yj_{2}=2+2y+xjj_{4}+3xj$$

The equation is in standard form.

$$yj_{2}=jj_{4}x+3jx+2y+2$$

Divide both sides by y.

$$\frac{yj_{2}}{y}=\frac{jj_{4}x+3jx+2y+2}{y}$$

Dividing by y undoes the multiplication by y.

$$j_{2}=\frac{jj_{4}x+3jx+2y+2}{y}$$

Solve for j

$$\left\{\begin{matrix}j=\frac{j_{2}y-2y-2}{x\left(j_{4}+3\right)}\text{, }&j_{4}\neq -3\text{ and }x\neq 0\\j\in \mathrm{R}\text{, }&y=\frac{2}{j_{2}-2}\text{ and }j_{2}\neq 2\text{ and }\left(j_{4}=-3\text{ or }x=0\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply y by j_{2}-2.

$$yj_{2}-2y-xj\left(j_{4}+3\right)=2$$

Use the distributive property to multiply xj by j_{4}+3.

$$yj_{2}-2y-\left(xjj_{4}+3xj\right)=2$$

To find the opposite of xjj_{4}+3xj, find the opposite of each term.

$$yj_{2}-2y-xjj_{4}-3xj=2$$

Subtract yj_{2} from both sides.

$$-2y-xjj_{4}-3xj=2-yj_{2}$$

Add 2y to both sides.

$$-xjj_{4}-3xj=2-yj_{2}+2y$$

Combine all terms containing j.

$$\left(-xj_{4}-3x\right)j=2-yj_{2}+2y$$

The equation is in standard form.

$$\left(-j_{4}x-3x\right)j=2+2y-j_{2}y$$

Divide both sides by -j_{4}x-3x.

$$\frac{\left(-j_{4}x-3x\right)j}{-j_{4}x-3x}=\frac{2+2y-j_{2}y}{-j_{4}x-3x}$$

Dividing by -j_{4}x-3x undoes the multiplication by -j_{4}x-3x.

$$j=\frac{2+2y-j_{2}y}{-j_{4}x-3x}$$

Divide 2-yj_{2}+2y by -j_{4}x-3x.

$$j=\frac{2+2y-j_{2}y}{-x\left(j_{4}+3\right)}$$

Solve for j_2

$$\left\{\begin{matrix}j_{2}=\frac{jj_{4}x+3jx+2y+2}{y}\text{, }&y\neq 0\\j_{2}\in \mathrm{R}\text{, }&j=-\frac{2}{x\left(j_{4}+3\right)}\text{ and }j_{4}\neq -3\text{ and }x\neq 0\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply y by j_{2}-2.

$$yj_{2}-2y-xj\left(j_{4}+3\right)=2$$

Use the distributive property to multiply xj by j_{4}+3.

$$yj_{2}-2y-\left(xjj_{4}+3xj\right)=2$$

To find the opposite of xjj_{4}+3xj, find the opposite of each term.

$$yj_{2}-2y-xjj_{4}-3xj=2$$

Add 2y to both sides.

$$yj_{2}-xjj_{4}-3xj=2+2y$$

Add xjj_{4} to both sides.

$$yj_{2}-3xj=2+2y+xjj_{4}$$

Add 3xj to both sides.

$$yj_{2}=2+2y+xjj_{4}+3xj$$

The equation is in standard form.

$$yj_{2}=jj_{4}x+3jx+2y+2$$

Divide both sides by y.

$$\frac{yj_{2}}{y}=\frac{jj_{4}x+3jx+2y+2}{y}$$

Dividing by y undoes the multiplication by y.

$$j_{2}=\frac{jj_{4}x+3jx+2y+2}{y}$$