Solve alpha=x/b+y/2b

$$\alpha = \frac { x } { b } + \frac { y } { 2 b }$$

Solve for b

$$\left\{\begin{matrix}b=\frac{2x+y}{2\alpha }\text{, }&x\neq -\frac{y}{2}\text{ and }\alpha \neq 0\\b\neq 0\text{, }&x=-\frac{y}{2}\text{ and }\alpha =0\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable b cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 2b, the least common multiple of b,2b.

$$\alpha \times 2b=2x+y$$

Reorder the terms.

$$2b\alpha =2x+y$$

The equation is in standard form.

$$2\alpha b=2x+y$$

Divide both sides by 2\alpha .

$$\frac{2\alpha b}{2\alpha }=\frac{2x+y}{2\alpha }$$

Dividing by 2\alpha undoes the multiplication by 2\alpha .

$$b=\frac{2x+y}{2\alpha }$$

Variable b cannot be equal to 0.

$$b=\frac{2x+y}{2\alpha }\text{, }b\neq 0$$

Solve for x

$$x=b\alpha -\frac{y}{2}$$

$$b\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2b, the least common multiple of b,2b.

$$\alpha \times 2b=2x+y$$

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

$$2x+y=\alpha \times 2b$$

Subtract y from both sides.

$$2x=\alpha \times 2b-y$$

The equation is in standard form.

$$2x=2b\alpha -y$$

Divide both sides by 2.

$$\frac{2x}{2}=\frac{2b\alpha -y}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$x=\frac{2b\alpha -y}{2}$$

Divide 2\alpha b-y by 2.

$$x=b\alpha -\frac{y}{2}$$