Solve y=2+bt/1-t

$$y = \frac { 2 + b t } { 1 - t }$$

Solve for b

$$\left\{\begin{matrix}b=-\frac{ty-y+2}{t}\text{, }&t\neq 0\text{ and }t\neq 1\\b\in \mathrm{R}\text{, }&t=0\text{ and }y=2\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by -t+1.

$$y\left(-t+1\right)=2+bt$$

Use the distributive property to multiply y by -t+1.

$$-yt+y=2+bt$$

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

$$2+bt=-yt+y$$

Subtract 2 from both sides.

$$bt=-yt+y-2$$

The equation is in standard form.

$$tb=-ty+y-2$$

Divide both sides by t.

$$\frac{tb}{t}=\frac{-ty+y-2}{t}$$

Dividing by t undoes the multiplication by t.

$$b=\frac{-ty+y-2}{t}$$

Solve for t

$$\left\{\begin{matrix}t=\frac{y-2}{y+b}\text{, }&b\neq -2\text{ and }y\neq -b\\t\neq 1\text{, }&y=2\text{ and }b=-2\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable t cannot be equal to 1 since division by zero is not defined. Multiply both sides of the equation by -t+1.

$$y\left(-t+1\right)=2+bt$$

Use the distributive property to multiply y by -t+1.

$$-yt+y=2+bt$$

Subtract bt from both sides.

$$-yt+y-bt=2$$

Subtract y from both sides.

$$-yt-bt=2-y$$

Combine all terms containing t.

$$\left(-y-b\right)t=2-y$$

Divide both sides by -y-b.

$$\frac{\left(-y-b\right)t}{-y-b}=\frac{2-y}{-y-b}$$

Dividing by -y-b undoes the multiplication by -y-b.

$$t=\frac{2-y}{-y-b}$$

Divide 2-y by -y-b.

$$t=-\frac{2-y}{y+b}$$

Variable t cannot be equal to 1.

$$t=-\frac{2-y}{y+b}\text{, }t\neq 1$$