Solve x-1/2-y-1/3=1/6

$$\frac { x - 1 } { 2 } - \frac { y - 1 } { 3 } = \frac { 1 } { 6 }$$

Solve for x

$$x=\frac{2\left(y+1\right)}{3}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 6, the least common multiple of 2,3,6.

$$3\left(x-1\right)-2\left(y-1\right)=1$$

Use the distributive property to multiply 3 by x-1.

$$3x-3-2\left(y-1\right)=1$$

Use the distributive property to multiply -2 by y-1.

$$3x-3-2y+2=1$$

Add -3 and 2 to get -1.

$$3x-1-2y=1$$

Add 1 to both sides.

$$3x-2y=1+1$$

Add 1 and 1 to get 2.

$$3x-2y=2$$

Add 2y to both sides.

$$3x=2+2y$$

The equation is in standard form.

$$3x=2y+2$$

Divide both sides by 3.

$$\frac{3x}{3}=\frac{2y+2}{3}$$

Dividing by 3 undoes the multiplication by 3.

$$x=\frac{2y+2}{3}$$

Solve for y

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

Steps for Solving Linear Equation

Multiply both sides of the equation by 6, the least common multiple of 2,3,6.

$$3\left(x-1\right)-2\left(y-1\right)=1$$

Use the distributive property to multiply 3 by x-1.

$$3x-3-2\left(y-1\right)=1$$

Use the distributive property to multiply -2 by y-1.

$$3x-3-2y+2=1$$

Add -3 and 2 to get -1.

$$3x-1-2y=1$$

Subtract 3x from both sides.

$$-1-2y=1-3x$$

Add 1 to both sides.

$$-2y=1-3x+1$$

Add 1 and 1 to get 2.

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

Divide both sides by -2.

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

Dividing by -2 undoes the multiplication by -2.

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

Divide 2-3x by -2.

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