Solve t(1-x)-(y-t)x=0

$$t ( 1 - x ) - ( y - t ) x = 0$$

Solve for x (complex solution)

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

Steps for Solving Linear Equation

Use the distributive property to multiply t by 1-x.

$$t-tx-\left(y-t\right)x=0$$

Use the distributive property to multiply y-t by x.

$$t-tx-\left(yx-tx\right)=0$$

To find the opposite of yx-tx, find the opposite of each term.

$$t-tx-yx+tx=0$$

Combine -tx and tx to get 0.

$$t-yx=0$$

Subtract t from both sides. Anything subtracted from zero gives its negation.

$$-yx=-t$$

Cancel out -1 on both sides.

$$yx=t$$

Divide both sides by y.

$$\frac{yx}{y}=\frac{t}{y}$$

Dividing by y undoes the multiplication by y.

$$x=\frac{t}{y}$$

Solve for t

$$t=xy$$

Solution Steps

Use the distributive property to multiply t by 1-x.

$$t-tx-\left(y-t\right)x=0$$

Use the distributive property to multiply y-t by x.

$$t-tx-\left(yx-tx\right)=0$$

To find the opposite of yx-tx, find the opposite of each term.

$$t-tx-yx+tx=0$$

Combine -tx and tx to get 0.

$$t-yx=0$$

Add yx to both sides. Anything plus zero gives itself.

$$t=yx$$

Solve for x

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

Steps for Solving Linear Equation

Use the distributive property to multiply t by 1-x.

$$t-tx-\left(y-t\right)x=0$$

Use the distributive property to multiply y-t by x.

$$t-tx-\left(yx-tx\right)=0$$

To find the opposite of yx-tx, find the opposite of each term.

$$t-tx-yx+tx=0$$

Combine -tx and tx to get 0.

$$t-yx=0$$

Subtract t from both sides. Anything subtracted from zero gives its negation.

$$-yx=-t$$

Cancel out -1 on both sides.

$$yx=t$$

Divide both sides by y.

$$\frac{yx}{y}=\frac{t}{y}$$

Dividing by y undoes the multiplication by y.

$$x=\frac{t}{y}$$