Solve y=-3/2x+2/3/frac{1{3}}

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

Solve for x

$$x=\frac{4-2y}{9}$$

Steps for Solving Linear Equation

Divide each term of -\frac{3}{2}x+\frac{2}{3} by \frac{1}{3} to get \frac{-\frac{3}{2}x}{\frac{1}{3}}+\frac{\frac{2}{3}}{\frac{1}{3}}.

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

Divide -\frac{3}{2}x by \frac{1}{3} to get -\frac{9}{2}x.

$$y=-\frac{9}{2}x+\frac{\frac{2}{3}}{\frac{1}{3}}$$

Divide \frac{2}{3} by \frac{1}{3} by multiplying \frac{2}{3} by the reciprocal of \frac{1}{3}.

$$y=-\frac{9}{2}x+\frac{2}{3}\times 3$$

Multiply \frac{2}{3} and 3 to get 2.

$$y=-\frac{9}{2}x+2$$

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

$$-\frac{9}{2}x+2=y$$

Subtract 2 from both sides.

$$-\frac{9}{2}x=y-2$$

Divide both sides of the equation by -\frac{9}{2}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{-\frac{9}{2}x}{-\frac{9}{2}}=\frac{y-2}{-\frac{9}{2}}$$

Dividing by -\frac{9}{2} undoes the multiplication by -\frac{9}{2}.

$$x=\frac{y-2}{-\frac{9}{2}}$$

Divide y-2 by -\frac{9}{2} by multiplying y-2 by the reciprocal of -\frac{9}{2}.

$$x=\frac{4-2y}{9}$$

Solve for y

$$y=-\frac{9x}{2}+2$$

Solution Steps

Divide each term of -\frac{3}{2}x+\frac{2}{3} by \frac{1}{3} to get \frac{-\frac{3}{2}x}{\frac{1}{3}}+\frac{\frac{2}{3}}{\frac{1}{3}}.

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

Divide -\frac{3}{2}x by \frac{1}{3} to get -\frac{9}{2}x.

$$y=-\frac{9}{2}x+\frac{\frac{2}{3}}{\frac{1}{3}}$$

Divide \frac{2}{3} by \frac{1}{3} by multiplying \frac{2}{3} by the reciprocal of \frac{1}{3}.

$$y=-\frac{9}{2}x+\frac{2}{3}\times 3$$

Multiply \frac{2}{3} and 3 to get 2.

$$y=-\frac{9}{2}x+2$$