Solve (x/24+1/9y)-(x/24+y/36)=1-1

$$( \frac { x } { 24 } + \frac { 1 } { 9 } y ) - ( \frac { x } { 24 } + \frac { y } { 36 } ) = 1 - 1$$

Solve for y

$$y=0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 72, the least common multiple of 24,9,36.

$$72\left(\frac{x}{24}+\frac{1}{9}y\right)-72\left(\frac{x}{24}+\frac{y}{36}\right)=72-72$$

Use the distributive property to multiply 72 by \frac{x}{24}+\frac{1}{9}y.

$$72\times \frac{x}{24}+8y-72\left(\frac{x}{24}+\frac{y}{36}\right)=72-72$$

Cancel out 24, the greatest common factor in 72 and 24.

$$3x+8y-72\left(\frac{x}{24}+\frac{y}{36}\right)=72-72$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 24 and 36 is 72. Multiply \frac{x}{24} times \frac{3}{3}. Multiply \frac{y}{36} times \frac{2}{2}.

$$3x+8y-72\left(\frac{3x}{72}+\frac{2y}{72}\right)=72-72$$

Since \frac{3x}{72} and \frac{2y}{72} have the same denominator, add them by adding their numerators.

$$3x+8y-72\times \frac{3x+2y}{72}=72-72$$

Express 72\times \frac{3x+2y}{72} as a single fraction.

$$3x+8y-\frac{72\left(3x+2y\right)}{72}=72-72$$

Cancel out 72 and 72.

$$3x+8y-\left(3x+2y\right)=72-72$$

To find the opposite of 3x+2y, find the opposite of each term.

$$3x+8y-3x-2y=72-72$$

Combine 3x and -3x to get 0.

$$8y-2y=72-72$$

Combine 8y and -2y to get 6y.

$$6y=72-72$$

Subtract 72 from 72 to get 0.

$$6y=0$$

Product of two numbers is equal to 0 if at least one of them is 0. Since 6 is not equal to 0, y must be equal to 0.

$$y=0$$

Solve for x (complex solution)

$$x\in \mathrm{C}$$

$$y=0$$

Solve for x

$$x\in \mathrm{R}$$

$$y=0$$