Solve a/x+b/y=3

$$\frac { a } { x } + \frac { b } { y } = 3$$

Solve for a

$$a=-\frac{x\left(b-3y\right)}{y}$$

$$x\neq 0\text{ and }y\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by xy, the least common multiple of x,y.

$$ya+xb=3xy$$

Subtract xb from both sides.

$$ya=3xy-xb$$

The equation is in standard form.

$$ya=3xy-bx$$

Divide both sides by y.

$$\frac{ya}{y}=\frac{x\left(3y-b\right)}{y}$$

Dividing by y undoes the multiplication by y.

$$a=\frac{x\left(3y-b\right)}{y}$$

Solve for b

$$b=-\frac{y\left(a-3x\right)}{x}$$

$$x\neq 0\text{ and }y\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by xy, the least common multiple of x,y.

$$ya+xb=3xy$$

Subtract ya from both sides.

$$xb=3xy-ya$$

The equation is in standard form.

$$xb=3xy-ay$$

Divide both sides by x.

$$\frac{xb}{x}=\frac{y\left(3x-a\right)}{x}$$

Dividing by x undoes the multiplication by x.

$$b=\frac{y\left(3x-a\right)}{x}$$