Solve a/4-y=4-x/b

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

Solve for a

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

$$y\neq 4\text{ and }b\neq 0$$

Steps for Solving Linear Equation

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

$$-ba=\left(y-4\right)\left(4-x\right)$$

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

$$-ba=4y-yx-16+4x$$

The equation is in standard form.

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

Divide both sides by -b.

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

Dividing by -b undoes the multiplication by -b.

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

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

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

Solve for b

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

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

$$-ba=\left(y-4\right)\left(4-x\right)$$

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

$$-ba=4y-yx-16+4x$$

The equation is in standard form.

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

Divide both sides by -a.

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

Dividing by -a undoes the multiplication by -a.

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

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

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

Variable b cannot be equal to 0.

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