Solve x+11/y+11=18/13

$$\frac { x + 11 } { y + 11 } = \frac { 18 } { 13 }$$

Solve for x

$$x=\frac{18y+55}{13}$$

$$y\neq -11$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 13\left(y+11\right), the least common multiple of y+11,13.

$$13\left(x+11\right)=18\left(y+11\right)$$

Use the distributive property to multiply 13 by x+11.

$$13x+143=18\left(y+11\right)$$

Use the distributive property to multiply 18 by y+11.

$$13x+143=18y+198$$

Subtract 143 from both sides.

$$13x=18y+198-143$$

Subtract 143 from 198 to get 55.

$$13x=18y+55$$

Divide both sides by 13.

$$\frac{13x}{13}=\frac{18y+55}{13}$$

Dividing by 13 undoes the multiplication by 13.

$$x=\frac{18y+55}{13}$$

Solve for y

$$y=\frac{13x-55}{18}$$

$$x\neq -11$$

Steps for Solving Linear Equation

Variable y cannot be equal to -11 since division by zero is not defined. Multiply both sides of the equation by 13\left(y+11\right), the least common multiple of y+11,13.

$$13\left(x+11\right)=18\left(y+11\right)$$

Use the distributive property to multiply 13 by x+11.

$$13x+143=18\left(y+11\right)$$

Use the distributive property to multiply 18 by y+11.

$$13x+143=18y+198$$

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

$$18y+198=13x+143$$

Subtract 198 from both sides.

$$18y=13x+143-198$$

Subtract 198 from 143 to get -55.

$$18y=13x-55$$

Divide both sides by 18.

$$\frac{18y}{18}=\frac{13x-55}{18}$$

Dividing by 18 undoes the multiplication by 18.

$$y=\frac{13x-55}{18}$$

Variable y cannot be equal to -11.

$$y=\frac{13x-55}{18}\text{, }y\neq -11$$