Solve T/x+1/2y=1/y

$$\frac { T } { x } + \frac { 1 } { 2 y } = \frac { 1 } { y }$$

Solve for T

$$T=\frac{x}{2y}$$

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

Steps for Solving Linear Equation

Multiply both sides of the equation by 2xy, the least common multiple of x,2y,y.

$$2yT+x=2x$$

Subtract x from both sides.

$$2yT=2x-x$$

Combine 2x and -x to get x.

$$2yT=x$$

Divide both sides by 2y.

$$\frac{2yT}{2y}=\frac{x}{2y}$$

Dividing by 2y undoes the multiplication by 2y.

$$T=\frac{x}{2y}$$

Solve for x

$$x=2Ty$$

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

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,2y,y.

$$2yT+x=2x$$

Subtract 2x from both sides.

$$2yT+x-2x=0$$

Combine x and -2x to get -x.

$$2yT-x=0$$

Subtract 2yT from both sides. Anything subtracted from zero gives its negation.

$$-x=-2yT$$

The equation is in standard form.

$$-x=-2Ty$$

Divide both sides by -1.

$$\frac{-x}{-1}=-\frac{2Ty}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$x=-\frac{2Ty}{-1}$$

Divide -2yT by -1.

$$x=2Ty$$

Variable x cannot be equal to 0.

$$x=2Ty\text{, }x\neq 0$$