How do you find a=(3b+c)+5b given b=<6,3> and c=<-4,8>?

Aug 31, 2016

$a = < 44 , 32 >$

Explanation:

We can simplify the given $\textcolor{red}{a} = \left(3 \textcolor{b l u e}{b} + \textcolor{g r e e n}{c}\right) + 5 \textcolor{b l u e}{b}$ a bit as:
$\textcolor{w h i t e}{\text{XXX}} \textcolor{red}{a} = 8 \textcolor{b l u e}{b} + \textcolor{g r e e n}{c}$

Given that $\textcolor{b l u e}{b} = \textcolor{b l u e}{< 6 , 3 >}$
then
$\textcolor{w h i t e}{\text{XXX}} \textcolor{b l u e}{8 b} = < 6 \cdot 8 , 3 \cdot 8 > = \textcolor{b l u e}{< 48 , 24 >}$

and given that color(green)(c)=color(green)( < -4, 8 >

we have
$\textcolor{w h i t e}{\text{XXX}} \textcolor{red}{a} = \textcolor{b l u e}{< 48 , 24 >} + \textcolor{g r e e n}{< - 4 , 8 >}$

$\textcolor{w h i t e}{\text{XXXX}} = < \textcolor{b l u e}{48} \textcolor{g r e e n}{- 4} , \textcolor{b l u e}{24} \textcolor{g r e e n}{+ 8} >$

$\textcolor{w h i t e}{\text{XXXX}} = < 44 , 32 >$