Solve x/b+y/a=2

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

Solve for a

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

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 b,a.

$$ax+by=2ab$$

Subtract 2ab from both sides.

$$ax+by-2ab=0$$

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

$$ax-2ab=-by$$

Combine all terms containing a.

$$\left(x-2b\right)a=-by$$

Divide both sides by x-2b.

$$\frac{\left(x-2b\right)a}{x-2b}=-\frac{by}{x-2b}$$

Dividing by x-2b undoes the multiplication by x-2b.

$$a=-\frac{by}{x-2b}$$

Variable a cannot be equal to 0.

$$a=-\frac{by}{x-2b}\text{, }a\neq 0$$

Solve for b

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

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 b,a.

$$ax+by=2ab$$

Subtract 2ab from both sides.

$$ax+by-2ab=0$$

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

$$by-2ab=-ax$$

Combine all terms containing b.

$$\left(y-2a\right)b=-ax$$

Divide both sides by y-2a.

$$\frac{\left(y-2a\right)b}{y-2a}=-\frac{ax}{y-2a}$$

Dividing by y-2a undoes the multiplication by y-2a.

$$b=-\frac{ax}{y-2a}$$

Variable b cannot be equal to 0.

$$b=-\frac{ax}{y-2a}\text{, }b\neq 0$$