Solve 5/x+8/y=5

$$\frac { 5 } { x } + \frac { 8 } { y } = 5$$

Solve for x

$$x=-\frac{5y}{8-5y}$$

$$y\neq 0\text{ and }y\neq \frac{8}{5}$$

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.

$$y\times 5+x\times 8=5xy$$

Subtract 5xy from both sides.

$$y\times 5+x\times 8-5xy=0$$

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

$$x\times 8-5xy=-y\times 5$$

Multiply -1 and 5 to get -5.

$$x\times 8-5xy=-5y$$

Combine all terms containing x.

$$\left(8-5y\right)x=-5y$$

Divide both sides by 8-5y.

$$\frac{\left(8-5y\right)x}{8-5y}=-\frac{5y}{8-5y}$$

Dividing by 8-5y undoes the multiplication by 8-5y.

$$x=-\frac{5y}{8-5y}$$

Variable x cannot be equal to 0.

$$x=-\frac{5y}{8-5y}\text{, }x\neq 0$$

Solve for y

$$y=-\frac{8x}{5\left(1-x\right)}$$

$$x\neq 0\text{ and }x\neq 1$$

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.

$$y\times 5+x\times 8=5xy$$

Subtract 5xy from both sides.

$$y\times 5+x\times 8-5xy=0$$

Subtract x\times 8 from both sides. Anything subtracted from zero gives its negation.

$$y\times 5-5xy=-x\times 8$$

Multiply -1 and 8 to get -8.

$$y\times 5-5xy=-8x$$

Combine all terms containing y.

$$\left(5-5x\right)y=-8x$$

Divide both sides by -5x+5.

$$\frac{\left(5-5x\right)y}{5-5x}=-\frac{8x}{5-5x}$$

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

$$y=-\frac{8x}{5-5x}$$

Divide -8x by -5x+5.

$$y=-\frac{8x}{5\left(1-x\right)}$$

Variable y cannot be equal to 0.

$$y=-\frac{8x}{5\left(1-x\right)}\text{, }y\neq 0$$