Solve 3/x+4/y=5

$$\frac { 3 } { x } + \frac { 4 } { y } = 5$$

Solve for x

$$x=-\frac{3y}{4-5y}$$

$$y\neq 0\text{ and }y\neq \frac{4}{5}$$

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.

$$y\times 3+x\times 4=5xy$$

Subtract 5xy from both sides.

$$y\times 3+x\times 4-5xy=0$$

Subtract y\times 3 from both sides. Anything subtracted from zero gives its negation.

$$x\times 4-5xy=-y\times 3$$

Multiply -1 and 3 to get -3.

$$x\times 4-5xy=-3y$$

Combine all terms containing x.

$$\left(4-5y\right)x=-3y$$

Divide both sides by 4-5y.

$$\frac{\left(4-5y\right)x}{4-5y}=-\frac{3y}{4-5y}$$

Dividing by 4-5y undoes the multiplication by 4-5y.

$$x=-\frac{3y}{4-5y}$$

Variable x cannot be equal to 0.

$$x=-\frac{3y}{4-5y}\text{, }x\neq 0$$

Solve for y

$$y=-\frac{4x}{3-5x}$$

$$x\neq 0\text{ and }x\neq \frac{3}{5}$$

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.

$$y\times 3+x\times 4=5xy$$

Subtract 5xy from both sides.

$$y\times 3+x\times 4-5xy=0$$

Subtract x\times 4 from both sides. Anything subtracted from zero gives its negation.

$$y\times 3-5xy=-x\times 4$$

Multiply -1 and 4 to get -4.

$$y\times 3-5xy=-4x$$

Combine all terms containing y.

$$\left(3-5x\right)y=-4x$$

Divide both sides by 3-5x.

$$\frac{\left(3-5x\right)y}{3-5x}=-\frac{4x}{3-5x}$$

Dividing by 3-5x undoes the multiplication by 3-5x.

$$y=-\frac{4x}{3-5x}$$

Variable y cannot be equal to 0.

$$y=-\frac{4x}{3-5x}\text{, }y\neq 0$$