Solve 24-x+y/4=3y-y+x/6

$$\frac { 24 - x + y } { 4 } = \frac { 3 y - y + x } { 6 }$$

Solve for x

$$x=\frac{72-y}{5}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 12, the least common multiple of 4,6.

$$3\left(24-x+y\right)=2\left(3y-y+x\right)$$

Use the distributive property to multiply 3 by 24-x+y.

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

Combine 3y and -y to get 2y.

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

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

$$72-3x+3y=4y+2x$$

Subtract 2x from both sides.

$$72-3x+3y-2x=4y$$

Combine -3x and -2x to get -5x.

$$72-5x+3y=4y$$

Subtract 72 from both sides.

$$-5x+3y=4y-72$$

Subtract 3y from both sides.

$$-5x=4y-72-3y$$

Combine 4y and -3y to get y.

$$-5x=y-72$$

Divide both sides by -5.

$$\frac{-5x}{-5}=\frac{y-72}{-5}$$

Dividing by -5 undoes the multiplication by -5.

$$x=\frac{y-72}{-5}$$

Divide y-72 by -5.

$$x=\frac{72-y}{5}$$

Solve for y

$$y=72-5x$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 12, the least common multiple of 4,6.

$$3\left(24-x+y\right)=2\left(3y-y+x\right)$$

Use the distributive property to multiply 3 by 24-x+y.

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

Combine 3y and -y to get 2y.

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

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

$$72-3x+3y=4y+2x$$

Subtract 4y from both sides.

$$72-3x+3y-4y=2x$$

Combine 3y and -4y to get -y.

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

Subtract 72 from both sides.

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

Add 3x to both sides.

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

Combine 2x and 3x to get 5x.

$$-y=5x-72$$

Divide both sides by -1.

$$\frac{-y}{-1}=\frac{5x-72}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$y=\frac{5x-72}{-1}$$

Divide 5x-72 by -1.

$$y=72-5x$$