Solve 24-x+y/4=39-y+x/6

$$\frac { 24 - x + y } { 4 } = \frac { 39 - y + x } { 6 }$$

Solve for x

$$x = -\frac{6}{5} = -1\frac{1}{5} = -1.2$$

Steps for Solving Linear Equation

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

$$3\left(24-x+y\right)=2\left(39-y+x\right)$$

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

$$72-3x+3y=2\left(39-y+x\right)$$

Use the distributive property to multiply 2 by 39-y+x.

$$72-3x+3y=78-2y+2x$$

Subtract 2x from both sides.

$$72-3x+3y-2x=78-2y$$

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

$$72-5x+3y=78-2y$$

Subtract 72 from both sides.

$$-5x+3y=78-2y-72$$

Subtract 72 from 78 to get 6.

$$-5x+3y=6-2y$$

Subtract 3y from both sides.

$$-5x=6-2y-3y$$

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

$$-5x=6-5y$$

Divide both sides by -5.

$$\frac{-5x}{-5}=\frac{6-5y}{-5}$$

Dividing by -5 undoes the multiplication by -5.

$$x=\frac{6-5y}{-5}$$

Divide 6-5y by -5.

$$x=y-\frac{6}{5}$$

Solve for y

$$y = \frac{6}{5} = 1\frac{1}{5} = 1.2$$

Steps for Solving Linear Equation

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

$$3\left(24-x+y\right)=2\left(39-y+x\right)$$

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

$$72-3x+3y=2\left(39-y+x\right)$$

Use the distributive property to multiply 2 by 39-y+x.

$$72-3x+3y=78-2y+2x$$

Add 2y to both sides.

$$72-3x+3y+2y=78+2x$$

Combine 3y and 2y to get 5y.

$$72-3x+5y=78+2x$$

Subtract 72 from both sides.

$$-3x+5y=78+2x-72$$

Subtract 72 from 78 to get 6.

$$-3x+5y=6+2x$$

Add 3x to both sides.

$$5y=6+2x+3x$$

Combine 2x and 3x to get 5x.

$$5y=6+5x$$

The equation is in standard form.

$$5y=5x+6$$

Divide both sides by 5.

$$\frac{5y}{5}=\frac{5x+6}{5}$$

Dividing by 5 undoes the multiplication by 5.

$$y=\frac{5x+6}{5}$$

Divide 6+5x by 5.

$$y=x+\frac{6}{5}$$