Solve {l}{6u-{(1/2u-2)}=u+3/10}{v=0}{text{Solvefor}wtext{where}}{w=v}

$$\left. \begin{array} { l } { 6 u - {(\frac{1}{2} u - 2)} = u + \frac{3}{10} }\\ { v = 0 }\\ { \text{Solve for } w \text{ where} } \\ { w = v } \end{array} \right.$$

Solve for u, v, w

$$w=0$$

Solution Steps

Consider the first equation. To find the opposite of \frac{1}{2}u-2, find the opposite of each term.

$$6u-\frac{1}{2}u+2=u+\frac{3}{10}$$

Combine 6u and -\frac{1}{2}u to get \frac{11}{2}u.

$$\frac{11}{2}u+2=u+\frac{3}{10}$$

Subtract u from both sides.

$$\frac{11}{2}u+2-u=\frac{3}{10}$$

Combine \frac{11}{2}u and -u to get \frac{9}{2}u.

$$\frac{9}{2}u+2=\frac{3}{10}$$

Subtract 2 from both sides.

$$\frac{9}{2}u=\frac{3}{10}-2$$

Subtract 2 from \frac{3}{10} to get -\frac{17}{10}.

$$\frac{9}{2}u=-\frac{17}{10}$$

Multiply both sides by \frac{2}{9}, the reciprocal of \frac{9}{2}.

$$u=-\frac{17}{10}\times \frac{2}{9}$$

Multiply -\frac{17}{10} and \frac{2}{9} to get -\frac{17}{45}.

$$u=-\frac{17}{45}$$

The system is now solved.

$$u=-\frac{17}{45} v=0 w=0$$