Solve {l}{V=4xy^2z+3z^2y,text{betermine}}{t(1,-1,1)}

$$\left. \begin{array} { l } { V = 4 x y ^ { 2 } z + 3 z ^ { 2 } y , \text { betermine } } \\ { t ( 1 , - 1,1 ) } \end{array} \right.$$

Solve for x

$$\left\{\begin{matrix}x=\frac{V-3yz^{2}}{4zy^{2}}\text{, }&z\neq 0\text{ and }y\neq 0\\x\in \mathrm{R}\text{, }&\left(y=0\text{ or }z=0\right)\text{ and }V=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$4xy^{2}z+3z^{2}y=V$$

Subtract 3z^{2}y from both sides.

$$4xy^{2}z=V-3z^{2}y$$

The equation is in standard form.

$$4zy^{2}x=V-3yz^{2}$$

Divide both sides by 4y^{2}z.

$$\frac{4zy^{2}x}{4zy^{2}}=\frac{V-3yz^{2}}{4zy^{2}}$$

Dividing by 4y^{2}z undoes the multiplication by 4y^{2}z.

$$x=\frac{V-3yz^{2}}{4zy^{2}}$$