Solve (y+6)=-11/9(x-3)

$$( y + 6 ) = - \frac { 11 } { 9 } ( x - 3 )$$

Solve for x

$$x=\frac{-9y-21}{11}$$

Steps for Solving Linear Equation

Use the distributive property to multiply -\frac{11}{9} by x-3.

$$y+6=-\frac{11}{9}x+\frac{11}{3}$$

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

$$-\frac{11}{9}x+\frac{11}{3}=y+6$$

Subtract \frac{11}{3} from both sides.

$$-\frac{11}{9}x=y+6-\frac{11}{3}$$

Subtract \frac{11}{3} from 6 to get \frac{7}{3}.

$$-\frac{11}{9}x=y+\frac{7}{3}$$

Divide both sides of the equation by -\frac{11}{9}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{-\frac{11}{9}x}{-\frac{11}{9}}=\frac{y+\frac{7}{3}}{-\frac{11}{9}}$$

Dividing by -\frac{11}{9} undoes the multiplication by -\frac{11}{9}.

$$x=\frac{y+\frac{7}{3}}{-\frac{11}{9}}$$

Divide y+\frac{7}{3} by -\frac{11}{9} by multiplying y+\frac{7}{3} by the reciprocal of -\frac{11}{9}.

$$x=\frac{-9y-21}{11}$$

Solve for y

$$y=-\frac{11x}{9}-\frac{7}{3}$$

Solution Steps

Use the distributive property to multiply -\frac{11}{9} by x-3.

$$y+6=-\frac{11}{9}x+\frac{11}{3}$$

Subtract 6 from both sides.

$$y=-\frac{11}{9}x+\frac{11}{3}-6$$

Subtract 6 from \frac{11}{3} to get -\frac{7}{3}.

$$y=-\frac{11}{9}x-\frac{7}{3}$$