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

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

Solve for x

$$x=\frac{3y+7}{2}$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{2}{3} by x-5.

$$y-1=\frac{2}{3}x-\frac{10}{3}$$

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

$$\frac{2}{3}x-\frac{10}{3}=y-1$$

Add \frac{10}{3} to both sides.

$$\frac{2}{3}x=y-1+\frac{10}{3}$$

Add -1 and \frac{10}{3} to get \frac{7}{3}.

$$\frac{2}{3}x=y+\frac{7}{3}$$

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

$$\frac{\frac{2}{3}x}{\frac{2}{3}}=\frac{y+\frac{7}{3}}{\frac{2}{3}}$$

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

$$x=\frac{y+\frac{7}{3}}{\frac{2}{3}}$$

Divide y+\frac{7}{3} by \frac{2}{3} by multiplying y+\frac{7}{3} by the reciprocal of \frac{2}{3}.

$$x=\frac{3y+7}{2}$$

Solve for y

$$y=\frac{2x-7}{3}$$

Solution Steps

Use the distributive property to multiply \frac{2}{3} by x-5.

$$y-1=\frac{2}{3}x-\frac{10}{3}$$

Add 1 to both sides.

$$y=\frac{2}{3}x-\frac{10}{3}+1$$

Add -\frac{10}{3} and 1 to get -\frac{7}{3}.

$$y=\frac{2}{3}x-\frac{7}{3}$$