Solve 13/x+1/2=18/y

$$\frac { 13 } { x } + \frac { 1 } { 2 } = \frac { 18 } { y }$$

Solve for x

$$x=-\frac{26y}{y-36}$$

$$y\neq 0\text{ and }y\neq 36$$

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 2xy, the least common multiple of x,2,y.

$$2y\times 13+2xy\times \frac{1}{2}=2x\times 18$$

Multiply 2 and 13 to get 26.

$$26y+2xy\times \frac{1}{2}=2x\times 18$$

Multiply 2 and \frac{1}{2} to get 1.

$$26y+xy=2x\times 18$$

Multiply 2 and 18 to get 36.

$$26y+xy=36x$$

Subtract 36x from both sides.

$$26y+xy-36x=0$$

Subtract 26y from both sides. Anything subtracted from zero gives its negation.

$$xy-36x=-26y$$

Combine all terms containing x.

$$\left(y-36\right)x=-26y$$

Divide both sides by y-36.

$$\frac{\left(y-36\right)x}{y-36}=-\frac{26y}{y-36}$$

Dividing by y-36 undoes the multiplication by y-36.

$$x=-\frac{26y}{y-36}$$

Variable x cannot be equal to 0.

$$x=-\frac{26y}{y-36}\text{, }x\neq 0$$

Solve for y

$$y=\frac{36x}{x+26}$$

$$x\neq 0\text{ and }x\neq -26$$

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 2xy, the least common multiple of x,2,y.

$$2y\times 13+2xy\times \frac{1}{2}=2x\times 18$$

Multiply 2 and 13 to get 26.

$$26y+2xy\times \frac{1}{2}=2x\times 18$$

Multiply 2 and \frac{1}{2} to get 1.

$$26y+xy=2x\times 18$$

Multiply 2 and 18 to get 36.

$$26y+xy=36x$$

Combine all terms containing y.

$$\left(26+x\right)y=36x$$

The equation is in standard form.

$$\left(x+26\right)y=36x$$

Divide both sides by x+26.

$$\frac{\left(x+26\right)y}{x+26}=\frac{36x}{x+26}$$

Dividing by x+26 undoes the multiplication by x+26.

$$y=\frac{36x}{x+26}$$

Variable y cannot be equal to 0.

$$y=\frac{36x}{x+26}\text{, }y\neq 0$$