Solve x/a+y/b=0

$$\frac { x } { a } + \frac { y } { b } = 0$$

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.

$$bx+ay=0$$

Subtract bx from both sides. Anything subtracted from zero gives its negation.

$$ay=-bx$$

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

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

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.

$$bx+ay=0$$

Subtract ay from both sides. Anything subtracted from zero gives its negation.

$$bx=-ay$$

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.

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