Solve x=3/7(kt+y)

$$x = \frac { 3 } { 7 } ( k t + y )$$

Solve for k (complex solution)

$$\left\{\begin{matrix}k=-\frac{3y-7x}{3t}\text{, }&t\neq 0\\k\in \mathrm{C}\text{, }&x=\frac{3y}{7}\text{ and }t=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{3}{7} by kt+y.

$$x=\frac{3}{7}kt+\frac{3}{7}y$$

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

$$\frac{3}{7}kt+\frac{3}{7}y=x$$

Subtract \frac{3}{7}y from both sides.

$$\frac{3}{7}kt=x-\frac{3}{7}y$$

The equation is in standard form.

$$\frac{3t}{7}k=-\frac{3y}{7}+x$$

Divide both sides by \frac{3}{7}t.

$$\frac{7\times \frac{3t}{7}k}{3t}=\frac{7\left(-\frac{3y}{7}+x\right)}{3t}$$

Dividing by \frac{3}{7}t undoes the multiplication by \frac{3}{7}t.

$$k=\frac{7\left(-\frac{3y}{7}+x\right)}{3t}$$

Divide x-\frac{3y}{7} by \frac{3}{7}t.

$$k=\frac{7x-3y}{3t}$$

Solve for t (complex solution)

$$\left\{\begin{matrix}t=-\frac{3y-7x}{3k}\text{, }&k\neq 0\\t\in \mathrm{C}\text{, }&x=\frac{3y}{7}\text{ and }k=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{3}{7} by kt+y.

$$x=\frac{3}{7}kt+\frac{3}{7}y$$

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

$$\frac{3}{7}kt+\frac{3}{7}y=x$$

Subtract \frac{3}{7}y from both sides.

$$\frac{3}{7}kt=x-\frac{3}{7}y$$

The equation is in standard form.

$$\frac{3k}{7}t=-\frac{3y}{7}+x$$

Divide both sides by \frac{3}{7}k.

$$\frac{7\times \frac{3k}{7}t}{3k}=\frac{7\left(-\frac{3y}{7}+x\right)}{3k}$$

Dividing by \frac{3}{7}k undoes the multiplication by \frac{3}{7}k.

$$t=\frac{7\left(-\frac{3y}{7}+x\right)}{3k}$$

Divide x-\frac{3y}{7} by \frac{3}{7}k.

$$t=\frac{7x-3y}{3k}$$

Solve for k

$$\left\{\begin{matrix}k=-\frac{3y-7x}{3t}\text{, }&t\neq 0\\k\in \mathrm{R}\text{, }&x=\frac{3y}{7}\text{ and }t=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{3}{7} by kt+y.

$$x=\frac{3}{7}kt+\frac{3}{7}y$$

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

$$\frac{3}{7}kt+\frac{3}{7}y=x$$

Subtract \frac{3}{7}y from both sides.

$$\frac{3}{7}kt=x-\frac{3}{7}y$$

The equation is in standard form.

$$\frac{3t}{7}k=-\frac{3y}{7}+x$$

Divide both sides by \frac{3}{7}t.

$$\frac{7\times \frac{3t}{7}k}{3t}=\frac{7\left(-\frac{3y}{7}+x\right)}{3t}$$

Dividing by \frac{3}{7}t undoes the multiplication by \frac{3}{7}t.

$$k=\frac{7\left(-\frac{3y}{7}+x\right)}{3t}$$

Divide x-\frac{3y}{7} by \frac{3}{7}t.

$$k=\frac{7x-3y}{3t}$$

Solve for t

$$\left\{\begin{matrix}t=-\frac{3y-7x}{3k}\text{, }&k\neq 0\\t\in \mathrm{R}\text{, }&x=\frac{3y}{7}\text{ and }k=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{3}{7} by kt+y.

$$x=\frac{3}{7}kt+\frac{3}{7}y$$

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

$$\frac{3}{7}kt+\frac{3}{7}y=x$$

Subtract \frac{3}{7}y from both sides.

$$\frac{3}{7}kt=x-\frac{3}{7}y$$

The equation is in standard form.

$$\frac{3k}{7}t=-\frac{3y}{7}+x$$

Divide both sides by \frac{3}{7}k.

$$\frac{7\times \frac{3k}{7}t}{3k}=\frac{7\left(-\frac{3y}{7}+x\right)}{3k}$$

Dividing by \frac{3}{7}k undoes the multiplication by \frac{3}{7}k.

$$t=\frac{7\left(-\frac{3y}{7}+x\right)}{3k}$$

Divide x-\frac{3y}{7} by \frac{3}{7}k.

$$t=\frac{7x-3y}{3k}$$