Solve x/a=y/bquad

$$\frac { x } { a } = \frac { y } { b } \quad$$

Solve for a

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

Steps for Solving Linear Equation

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

$$bx=ay$$

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

$$ay=bx$$

The equation is in standard form.

$$ya=bx$$

Divide both sides by y.

$$\frac{ya}{y}=\frac{bx}{y}$$

Dividing by y undoes the multiplication by y.

$$a=\frac{bx}{y}$$

Variable a cannot be equal to 0.

$$a=\frac{bx}{y}\text{, }a\neq 0$$

Solve for b

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

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 ab, the least common multiple of a,b.

$$bx=ay$$

The equation is in standard form.

$$xb=ay$$

Divide both sides by x.

$$\frac{xb}{x}=\frac{ay}{x}$$

Dividing by x undoes the multiplication by x.

$$b=\frac{ay}{x}$$

Variable b cannot be equal to 0.

$$b=\frac{ay}{x}\text{, }b\neq 0$$