Solve 5/x+6/y=1

$$\frac { 5 } { x } + \frac { 6 } { y } = 1$$

Solve for x

$$x=-\frac{5y}{6-y}$$

$$y\neq 0\text{ and }y\neq 6$$

Steps for Solving Linear Equation

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

$$y\times 5+x\times 6=xy$$

Subtract xy from both sides.

$$y\times 5+x\times 6-xy=0$$

Subtract y\times 5 from both sides. Anything subtracted from zero gives its negation.

$$x\times 6-xy=-y\times 5$$

Multiply -1 and 5 to get -5.

$$x\times 6-xy=-5y$$

Combine all terms containing x.

$$\left(6-y\right)x=-5y$$

Divide both sides by 6-y.

$$\frac{\left(6-y\right)x}{6-y}=-\frac{5y}{6-y}$$

Dividing by 6-y undoes the multiplication by 6-y.

$$x=-\frac{5y}{6-y}$$

Variable x cannot be equal to 0.

$$x=-\frac{5y}{6-y}\text{, }x\neq 0$$

Solve for y

$$y=-\frac{6x}{5-x}$$

$$x\neq 0\text{ and }x\neq 5$$

Steps for Solving Linear Equation

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

$$y\times 5+x\times 6=xy$$

Subtract xy from both sides.

$$y\times 5+x\times 6-xy=0$$

Subtract x\times 6 from both sides. Anything subtracted from zero gives its negation.

$$y\times 5-xy=-x\times 6$$

Multiply -1 and 6 to get -6.

$$y\times 5-xy=-6x$$

Combine all terms containing y.

$$\left(5-x\right)y=-6x$$

Divide both sides by 5-x.

$$\frac{\left(5-x\right)y}{5-x}=-\frac{6x}{5-x}$$

Dividing by 5-x undoes the multiplication by 5-x.

$$y=-\frac{6x}{5-x}$$

Variable y cannot be equal to 0.

$$y=-\frac{6x}{5-x}\text{, }y\neq 0$$