Solve x+y/2-x-y/4=1

$$\frac { x + y } { 2 } - \frac { x - y } { 4 } = 1$$

Solve for x

$$x=4-3y$$

Solution Steps

Multiply both sides of the equation by 4, the least common multiple of 2,4.

$$2\left(x+y\right)-\left(x-y\right)=4$$

Use the distributive property to multiply 2 by x+y.

$$2x+2y-\left(x-y\right)=4$$

To find the opposite of x-y, find the opposite of each term.

$$2x+2y-x+y=4$$

Combine 2x and -x to get x.

$$x+2y+y=4$$

Combine 2y and y to get 3y.

$$x+3y=4$$

Subtract 3y from both sides.

$$x=4-3y$$

Solve for y

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

Steps for Solving Linear Equation

Multiply both sides of the equation by 4, the least common multiple of 2,4.

$$2\left(x+y\right)-\left(x-y\right)=4$$

Use the distributive property to multiply 2 by x+y.

$$2x+2y-\left(x-y\right)=4$$

To find the opposite of x-y, find the opposite of each term.

$$2x+2y-x+y=4$$

Combine 2x and -x to get x.

$$x+2y+y=4$$

Combine 2y and y to get 3y.

$$x+3y=4$$

Subtract x from both sides.

$$3y=4-x$$

Divide both sides by 3.

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

Dividing by 3 undoes the multiplication by 3.

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