Solve 2/3x-3/4y=1/6

$$\frac { 2 } { 3 } x - \frac { 3 } { 4 } y = \frac { 1 } { 6 }$$

Solve for x

$$x=\frac{9y}{8}+\frac{1}{4}$$

Steps for Solving Linear Equation

Add \frac{3}{4}y to both sides.

$$\frac{2}{3}x=\frac{1}{6}+\frac{3}{4}y$$

The equation is in standard form.

$$\frac{2}{3}x=\frac{3y}{4}+\frac{1}{6}$$

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

$$\frac{\frac{2}{3}x}{\frac{2}{3}}=\frac{\frac{3y}{4}+\frac{1}{6}}{\frac{2}{3}}$$

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

$$x=\frac{\frac{3y}{4}+\frac{1}{6}}{\frac{2}{3}}$$

Divide \frac{1}{6}+\frac{3y}{4} by \frac{2}{3} by multiplying \frac{1}{6}+\frac{3y}{4} by the reciprocal of \frac{2}{3}.

$$x=\frac{9y}{8}+\frac{1}{4}$$

Solve for y

$$y=\frac{8x-2}{9}$$

Steps for Solving Linear Equation

Subtract \frac{2}{3}x from both sides.

$$-\frac{3}{4}y=\frac{1}{6}-\frac{2}{3}x$$

The equation is in standard form.

$$-\frac{3}{4}y=-\frac{2x}{3}+\frac{1}{6}$$

Divide both sides of the equation by -\frac{3}{4}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{-\frac{3}{4}y}{-\frac{3}{4}}=\frac{-\frac{2x}{3}+\frac{1}{6}}{-\frac{3}{4}}$$

Dividing by -\frac{3}{4} undoes the multiplication by -\frac{3}{4}.

$$y=\frac{-\frac{2x}{3}+\frac{1}{6}}{-\frac{3}{4}}$$

Divide \frac{1}{6}-\frac{2x}{3} by -\frac{3}{4} by multiplying \frac{1}{6}-\frac{2x}{3} by the reciprocal of -\frac{3}{4}.

$$y=\frac{8x-2}{9}$$