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

$$\frac { x - y } { 3 } - \frac { x - 2 y } { 4 } = \frac { x - 3 } { 12 }$$

Solve for y

$$y = -\frac{3}{2} = -1\frac{1}{2} = -1.5$$

Steps for Solving Linear Equation

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

$$4\left(x-y\right)-3\left(x-2y\right)=x-3$$

Use the distributive property to multiply 4 by x-y.

$$4x-4y-3\left(x-2y\right)=x-3$$

Use the distributive property to multiply -3 by x-2y.

$$4x-4y-3x+6y=x-3$$

Combine 4x and -3x to get x.

$$x-4y+6y=x-3$$

Combine -4y and 6y to get 2y.

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

Subtract x from both sides.

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

Combine x and -x to get 0.

$$2y=-3$$

Divide both sides by 2.

$$y=\frac{-3}{2}$$

Fraction \frac{-3}{2} can be rewritten as -\frac{3}{2} by extracting the negative sign.

$$y=-\frac{3}{2}$$

Solve for x (complex solution)

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

$$y = -\frac{3}{2} = -1\frac{1}{2} = -1.5$$

Solve for x

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

$$y = -\frac{3}{2} = -1\frac{1}{2} = -1.5$$