Solve 5-y/6-x=-2

$$\frac { 5 - y } { 6 - x } = - 2$$

Solve for x

$$x=\frac{17-y}{2}$$

$$y\neq 5$$

Steps for Solving Linear Equation

Variable x cannot be equal to 6 since division by zero is not defined. Multiply both sides of the equation by -x+6.

$$5-y=-2\left(-x+6\right)$$

Use the distributive property to multiply -2 by -x+6.

$$5-y=2x-12$$

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

$$2x-12=5-y$$

Add 12 to both sides.

$$2x=5-y+12$$

Add 5 and 12 to get 17.

$$2x=17-y$$

Divide both sides by 2.

$$\frac{2x}{2}=\frac{17-y}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$x=\frac{17-y}{2}$$

Variable x cannot be equal to 6.

$$x=\frac{17-y}{2}\text{, }x\neq 6$$

Solve for y

$$y=17-2x$$

$$x\neq 6$$

Steps for Solving Linear Equation

Multiply both sides of the equation by -x+6.

$$5-y=-2\left(-x+6\right)$$

Use the distributive property to multiply -2 by -x+6.

$$5-y=2x-12$$

Subtract 5 from both sides.

$$-y=2x-12-5$$

Subtract 5 from -12 to get -17.

$$-y=2x-17$$

Divide both sides by -1.

$$\frac{-y}{-1}=\frac{2x-17}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$y=\frac{2x-17}{-1}$$

Divide 2x-17 by -1.

$$y=17-2x$$