Solve za/4-y=4-x/2b

$$\frac { z a } { 4 - y } = \frac { 4 - x } { 2 b }$$

Solve for a

$$\left\{\begin{matrix}a=-\frac{\left(4-y\right)\left(x-4\right)}{2bz}\text{, }&b\neq 0\text{ and }z\neq 0\text{ and }y\neq 4\\a\in \mathrm{R}\text{, }&x=4\text{ and }z=0\text{ and }b\neq 0\text{ and }y\neq 4\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2b\left(y-4\right), the least common multiple of 4-y,2b.

$$-2bza=\left(y-4\right)\left(4-x\right)$$

Use the distributive property to multiply y-4 by 4-x.

$$-2bza=4y-yx-16+4x$$

The equation is in standard form.

$$\left(-2bz\right)a=-xy+4x+4y-16$$

Divide both sides by -2bz.

$$\frac{\left(-2bz\right)a}{-2bz}=\frac{\left(4-y\right)\left(x-4\right)}{-2bz}$$

Dividing by -2bz undoes the multiplication by -2bz.

$$a=\frac{\left(4-y\right)\left(x-4\right)}{-2bz}$$

Divide \left(-4+x\right)\left(4-y\right) by -2bz.

$$a=-\frac{\left(4-y\right)\left(x-4\right)}{2bz}$$

Solve for b

$$\left\{\begin{matrix}b=-\frac{\left(4-y\right)\left(x-4\right)}{2az}\text{, }&y\neq 4\text{ and }x\neq 4\text{ and }a\neq 0\text{ and }z\neq 0\\b\neq 0\text{, }&\left(a=0\text{ or }z=0\right)\text{ and }x=4\text{ and }y\neq 4\end{matrix}\right.$$

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\left(y-4\right), the least common multiple of 4-y,2b.

$$-2bza=\left(y-4\right)\left(4-x\right)$$

Use the distributive property to multiply y-4 by 4-x.

$$-2bza=4y-yx-16+4x$$

The equation is in standard form.

$$\left(-2az\right)b=-xy+4x+4y-16$$

Divide both sides by -2za.

$$\frac{\left(-2az\right)b}{-2az}=\frac{\left(4-y\right)\left(x-4\right)}{-2az}$$

Dividing by -2za undoes the multiplication by -2za.

$$b=\frac{\left(4-y\right)\left(x-4\right)}{-2az}$$

Divide \left(-4+x\right)\left(4-y\right) by -2za.

$$b=-\frac{\left(4-y\right)\left(x-4\right)}{2az}$$

Variable b cannot be equal to 0.

$$b=-\frac{\left(4-y\right)\left(x-4\right)}{2az}\text{, }b\neq 0$$