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

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

Solve for x

$$x=\frac{2y}{3}-\frac{11}{15}$$

Steps for Solving Linear Equation

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

$$y-\frac{1}{5}=\frac{3}{2}x+\frac{9}{10}$$

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

$$\frac{3}{2}x+\frac{9}{10}=y-\frac{1}{5}$$

Subtract \frac{9}{10} from both sides.

$$\frac{3}{2}x=y-\frac{1}{5}-\frac{9}{10}$$

Subtract \frac{9}{10} from -\frac{1}{5} to get -\frac{11}{10}.

$$\frac{3}{2}x=y-\frac{11}{10}$$

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

$$\frac{\frac{3}{2}x}{\frac{3}{2}}=\frac{y-\frac{11}{10}}{\frac{3}{2}}$$

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

$$x=\frac{y-\frac{11}{10}}{\frac{3}{2}}$$

Divide y-\frac{11}{10} by \frac{3}{2} by multiplying y-\frac{11}{10} by the reciprocal of \frac{3}{2}.

$$x=\frac{2y}{3}-\frac{11}{15}$$

Solve for y

$$y=\frac{3x}{2}+\frac{11}{10}$$

Solution Steps

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

$$y-\frac{1}{5}=\frac{3}{2}x+\frac{9}{10}$$

Add \frac{1}{5} to both sides.

$$y=\frac{3}{2}x+\frac{9}{10}+\frac{1}{5}$$

Add \frac{9}{10} and \frac{1}{5} to get \frac{11}{10}.

$$y=\frac{3}{2}x+\frac{11}{10}$$