Solve 3/v-3=y/v-3+7

$$\frac { 3 } { v - 3 } = \frac { y } { v - 3 } + 7$$

Solve for v

$$v=\frac{24-y}{7}$$

$$y\neq 3$$

Steps for Solving Linear Equation

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

$$3=y+\left(v-3\right)\times 7$$

Use the distributive property to multiply v-3 by 7.

$$3=y+7v-21$$

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

$$y+7v-21=3$$

Subtract y from both sides.

$$7v-21=3-y$$

Add 21 to both sides.

$$7v=3-y+21$$

Add 3 and 21 to get 24.

$$7v=24-y$$

Divide both sides by 7.

$$\frac{7v}{7}=\frac{24-y}{7}$$

Dividing by 7 undoes the multiplication by 7.

$$v=\frac{24-y}{7}$$

Variable v cannot be equal to 3.

$$v=\frac{24-y}{7}\text{, }v\neq 3$$

Solve for y

$$y=24-7v$$

$$v\neq 3$$

Solution Steps

Multiply both sides of the equation by v-3.

$$3=y+\left(v-3\right)\times 7$$

Use the distributive property to multiply v-3 by 7.

$$3=y+7v-21$$

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

$$y+7v-21=3$$

Subtract 7v from both sides.

$$y-21=3-7v$$

Add 21 to both sides.

$$y=3-7v+21$$

Add 3 and 21 to get 24.

$$y=24-7v$$