Solve 2/3a-1/3b=2

$$\frac { 2 } { 3 } a - \frac { 1 } { 3 } b = 2$$

Solve for a

$$a=\frac{b+6}{2}$$

Steps for Solving Linear Equation

Add \frac{1}{3}b to both sides.

$$\frac{2}{3}a=2+\frac{1}{3}b$$

The equation is in standard form.

$$\frac{2}{3}a=\frac{b}{3}+2$$

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

$$\frac{\frac{2}{3}a}{\frac{2}{3}}=\frac{\frac{b}{3}+2}{\frac{2}{3}}$$

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

$$a=\frac{\frac{b}{3}+2}{\frac{2}{3}}$$

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

$$a=\frac{b}{2}+3$$

Solve for b

$$b=2\left(a-3\right)$$

Steps for Solving Linear Equation

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

$$-\frac{1}{3}b=2-\frac{2}{3}a$$

The equation is in standard form.

$$-\frac{1}{3}b=-\frac{2a}{3}+2$$

Multiply both sides by -3.

$$\frac{-\frac{1}{3}b}{-\frac{1}{3}}=\frac{-\frac{2a}{3}+2}{-\frac{1}{3}}$$

Dividing by -\frac{1}{3} undoes the multiplication by -\frac{1}{3}.

$$b=\frac{-\frac{2a}{3}+2}{-\frac{1}{3}}$$

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

$$b=2a-6$$