Solve y-5=-2/3(x+1)

$$y - 5 = - \frac { 2 } { 3 } ( x + 1 )$$

Solve for x

$$x=\frac{13-3y}{2}$$

Steps for Solving Linear Equation

Use the distributive property to multiply -\frac{2}{3} by x+1.

$$y-5=-\frac{2}{3}x-\frac{2}{3}$$

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

$$-\frac{2}{3}x-\frac{2}{3}=y-5$$

Add \frac{2}{3} to both sides.

$$-\frac{2}{3}x=y-5+\frac{2}{3}$$

Add -5 and \frac{2}{3} to get -\frac{13}{3}.

$$-\frac{2}{3}x=y-\frac{13}{3}$$

Divide both sides of the equation by -\frac{2}{3}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{-\frac{2}{3}x}{-\frac{2}{3}}=\frac{y-\frac{13}{3}}{-\frac{2}{3}}$$

Dividing by -\frac{2}{3} undoes the multiplication by -\frac{2}{3}.

$$x=\frac{y-\frac{13}{3}}{-\frac{2}{3}}$$

Divide y-\frac{13}{3} by -\frac{2}{3} by multiplying y-\frac{13}{3} by the reciprocal of -\frac{2}{3}.

$$x=\frac{13-3y}{2}$$

Solve for y

$$y=\frac{13-2x}{3}$$

Solution Steps

Use the distributive property to multiply -\frac{2}{3} by x+1.

$$y-5=-\frac{2}{3}x-\frac{2}{3}$$

Add 5 to both sides.

$$y=-\frac{2}{3}x-\frac{2}{3}+5$$

Add -\frac{2}{3} and 5 to get \frac{13}{3}.

$$y=-\frac{2}{3}x+\frac{13}{3}$$