How to Solve Vector Equations

You put the expressions in front of $\overrightarrow{u}$ equal to each other and the expressions in front of $\overrightarrow{v}$ equal to each other. Then you can solve the set of equations:

$$\begin{array}{llllllll}\hfill 2-k& =4& \hfill 1& =-l-3& \hfill & & \hfill & \\ \hfill k& =-2& \hfill l& =-4& \hfill & & \hfill & \end{array}$$

You put the expressions in front of $\overrightarrow{u}$ equal to each other and the expressions in front of $\overrightarrow{v}$ equal to each other. That gives you this system of equations, which you can solve:

$$\begin{array}{llllllll}\hfill l+3k& =2k& \hfill 3& =-4-2k& \hfill & & \hfill & \\ \hfill & & \hfill 7& =-2k& \hfill & & \hfill & \\ \hfill & & \hfill k& =-\frac{7}{2}& \hfill & & \hfill & \\ \hfill l& =-k& \hfill & & \hfill & & \hfill & \\ \hfill l& =-\left(-\frac{7}{2}\right)& \hfill & & \hfill & & \hfill & \\ \hfill l& =\frac{7}{2}& \hfill & & \hfill & \end{array}$$