Chapter 7 - Section 7.5 - Vectors: An Algebraic Approach - 7.5 Problem Set - Page 405: 47

\begin{align*} U+V&=6i-8j.\\ U-V&=6i+8j.\\ 3U+2V&=18i-16j. \end{align*}

We have $U=6i, V=-8j.$ First find $U+V$, \begin{align*} U+V&=6i+(-8j)\\ &=6i-8j. \end{align*} Hence, $U+V=26i-8j.$ Then find $U-V$, \begin{align*} U-V&=6i-(-8j)\\ &=6i+8j. \end{align*} Hence, $U-V=6i+8j.$ In the end find, \begin{align*} 3U+2V&=3(6i)+2(-8j)\\ &=18i-16j. \end{align*}