Solve 1/2u+1/3v=2

$$\frac { 1 } { 2 } u + \frac { 1 } { 3 } v = 2$$

Solve for u

$$u=-\frac{2v}{3}+4$$

Steps for Solving Linear Equation

Subtract \frac{1}{3}v from both sides.

$$\frac{1}{2}u=2-\frac{1}{3}v$$

The equation is in standard form.

$$\frac{1}{2}u=-\frac{v}{3}+2$$

Multiply both sides by 2.

$$\frac{\frac{1}{2}u}{\frac{1}{2}}=\frac{-\frac{v}{3}+2}{\frac{1}{2}}$$

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

$$u=\frac{-\frac{v}{3}+2}{\frac{1}{2}}$$

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

$$u=-\frac{2v}{3}+4$$

Solve for v

$$v=-\frac{3u}{2}+6$$

Steps for Solving Linear Equation

Subtract \frac{1}{2}u from both sides.

$$\frac{1}{3}v=2-\frac{1}{2}u$$

The equation is in standard form.

$$\frac{1}{3}v=-\frac{u}{2}+2$$

Multiply both sides by 3.

$$\frac{\frac{1}{3}v}{\frac{1}{3}}=\frac{-\frac{u}{2}+2}{\frac{1}{3}}$$

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

$$v=\frac{-\frac{u}{2}+2}{\frac{1}{3}}$$

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

$$v=-\frac{3u}{2}+6$$