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

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

Solve for x

$$x=6-y$$

$$y\neq 3$$

Solution Steps

Multiply both sides of the equation by y-3.

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

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

$$x-3=2y-6+\left(y-3\right)\left(-3\right)$$

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

$$x-3=2y-6-3y+9$$

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

$$x-3=-y-6+9$$

Add -6 and 9 to get 3.

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

Add 3 to both sides.

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

Add 3 and 3 to get 6.

$$x=-y+6$$

Solve for y

$$y=6-x$$

$$x\neq 3$$

Steps for Solving Linear Equation

Variable y cannot be equal to 3 since division by zero is not defined. Multiply both sides of the equation by y-3.

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

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

$$x-3=2y-6+\left(y-3\right)\left(-3\right)$$

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

$$x-3=2y-6-3y+9$$

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

$$x-3=-y-6+9$$

Add -6 and 9 to get 3.

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

Swap sides so that all variable terms are on the left hand side.

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

Subtract 3 from both sides.

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

Subtract 3 from -3 to get -6.

$$-y=x-6$$

Divide both sides by -1.

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

Dividing by -1 undoes the multiplication by -1.

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

Divide x-6 by -1.

$$y=6-x$$

Variable y cannot be equal to 3.

$$y=6-x\text{, }y\neq 3$$