Solve x/5+5/y=10

$$\frac { x } { 5 } + \frac { 5 } { y } = 10$$

Solve for x

$$x=50-\frac{25}{y}$$

$$y\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 5y, the least common multiple of 5,y.

$$yx+5\times 5=50y$$

Multiply 5 and 5 to get 25.

$$yx+25=50y$$

Subtract 25 from both sides.

$$yx=50y-25$$

Divide both sides by y.

$$\frac{yx}{y}=\frac{50y-25}{y}$$

Dividing by y undoes the multiplication by y.

$$x=\frac{50y-25}{y}$$

Divide 50y-25 by y.

$$x=50-\frac{25}{y}$$

Solve for y

$$y=-\frac{25}{x-50}$$

$$x\neq 50$$

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 5y, the least common multiple of 5,y.

$$yx+5\times 5=50y$$

Multiply 5 and 5 to get 25.

$$yx+25=50y$$

Subtract 50y from both sides.

$$yx+25-50y=0$$

Subtract 25 from both sides. Anything subtracted from zero gives its negation.

$$yx-50y=-25$$

Combine all terms containing y.

$$\left(x-50\right)y=-25$$

Divide both sides by -50+x.

$$\frac{\left(x-50\right)y}{x-50}=-\frac{25}{x-50}$$

Dividing by -50+x undoes the multiplication by -50+x.

$$y=-\frac{25}{x-50}$$

Variable y cannot be equal to 0.

$$y=-\frac{25}{x-50}\text{, }y\neq 0$$