Solve -1/2a+4/3b=-7/3

$$- \frac{ 1 }{ 2 } a+ \frac{ 4 }{ 3 } b = - \frac{ 7 }{ 3 }$$

Solve for a

$$a=\frac{8b+14}{3}$$

Steps for Solving Linear Equation

Subtract \frac{4}{3}b from both sides.

$$-\frac{1}{2}a=-\frac{7}{3}-\frac{4}{3}b$$

The equation is in standard form.

$$-\frac{1}{2}a=\frac{-4b-7}{3}$$

Multiply both sides by -2.

$$\frac{-\frac{1}{2}a}{-\frac{1}{2}}=\frac{-4b-7}{-\frac{1}{2}\times 3}$$

Dividing by -\frac{1}{2} undoes the multiplication by -\frac{1}{2}.

$$a=\frac{-4b-7}{-\frac{1}{2}\times 3}$$

Divide \frac{-7-4b}{3} by -\frac{1}{2} by multiplying \frac{-7-4b}{3} by the reciprocal of -\frac{1}{2}.

$$a=\frac{8b+14}{3}$$

Solve for b

$$b=\frac{3a}{8}-\frac{7}{4}$$

Steps for Solving Linear Equation

Add \frac{1}{2}a to both sides.

$$\frac{4}{3}b=-\frac{7}{3}+\frac{1}{2}a$$

The equation is in standard form.

$$\frac{4}{3}b=\frac{a}{2}-\frac{7}{3}$$

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

$$\frac{\frac{4}{3}b}{\frac{4}{3}}=\frac{\frac{a}{2}-\frac{7}{3}}{\frac{4}{3}}$$

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

$$b=\frac{\frac{a}{2}-\frac{7}{3}}{\frac{4}{3}}$$

Divide -\frac{7}{3}+\frac{a}{2} by \frac{4}{3} by multiplying -\frac{7}{3}+\frac{a}{2} by the reciprocal of \frac{4}{3}.

$$b=\frac{3a}{8}-\frac{7}{4}$$