Solve x/3-y/4=2x-y+12

$$x / 3 - y / 4 = 2 x - y + 12$$

Solve for x

$$x=\frac{9\left(y-16\right)}{20}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 12, the least common multiple of 3,4.

$$4x-3y=24x-12y+144$$

Subtract 24x from both sides.

$$4x-3y-24x=-12y+144$$

Combine 4x and -24x to get -20x.

$$-20x-3y=-12y+144$$

Add 3y to both sides.

$$-20x=-12y+144+3y$$

Combine -12y and 3y to get -9y.

$$-20x=-9y+144$$

The equation is in standard form.

$$-20x=144-9y$$

Divide both sides by -20.

$$\frac{-20x}{-20}=\frac{144-9y}{-20}$$

Dividing by -20 undoes the multiplication by -20.

$$x=\frac{144-9y}{-20}$$

Divide -9y+144 by -20.

$$x=\frac{9y}{20}-\frac{36}{5}$$

Solve for y

$$y=\frac{20x}{9}+16$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 12, the least common multiple of 3,4.

$$4x-3y=24x-12y+144$$

Add 12y to both sides.

$$4x-3y+12y=24x+144$$

Combine -3y and 12y to get 9y.

$$4x+9y=24x+144$$

Subtract 4x from both sides.

$$9y=24x+144-4x$$

Combine 24x and -4x to get 20x.

$$9y=20x+144$$

Divide both sides by 9.

$$\frac{9y}{9}=\frac{20x+144}{9}$$

Dividing by 9 undoes the multiplication by 9.

$$y=\frac{20x+144}{9}$$

Divide 20x+144 by 9.

$$y=\frac{20x}{9}+16$$