Answer
$a=5-\frac{8}{3}=\frac{7}{3}$
Work Step by Step
Vectors on first line are: $\left[\begin{array}{c}x \\ 2 x\end{array}\right]$ and vectors on second line are $\left[\begin{array}{c}x \\ 0.5 x\end{array}\right]$.
So, we are looking for a linear combination of vectors $\left[\begin{array}{l}1 \\ 2\end{array}\right]$ and $\left[\begin{array}{c}1 \\ 0.5\end{array}\right]$ so that $a\left[\begin{array}{l}1 \\ 2\end{array}\right]+b\left[\begin{array}{c}1 \\ 0.5\end{array}\right]=\left[\begin{array}{l}5 \\ 6\end{array}\right]$
Now find coefficients $a$ and $b$ :
$a+b=5$
$2 a+0.5 b=6$
Multiply first eq with - 2 and add to second:
$2 a+0.5 b-2 a-2 b=6-10$
$-1.5 b=-4$
$b=\frac{4}{3 / 2}=\frac{8}{3}$
$a+b=5$
$a=5-\frac{8}{3}=\frac{7}{3}$
