Question
Find $x$ and $y$ if $x\left[\begin{array}{c}4 \\ -3\end{array}\right]+y\left[\begin{array}{c}-2 \\ 3\end{array}\right]=\left[\begin{array}{l}4 \\ 6\end{array}\right]$
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Answer
$ \begin{aligned} & x\left[\begin{array}{c} 4 \\ -3 \end{array}\right]+y\left[\begin{array}{c} -2 \\ 3 \end{array}\right]=\left[\begin{array}{l} 4 \\ 6 \end{array}\right] \\ \\\end{aligned}$
${\left[\begin{array}{c} 4 x \\ -3 x \end{array}\right]+\left[\begin{array}{c} -2 y \\ 3 y \end{array}\right]=\left[\begin{array}{l} 4 \\ 6 \end{array}\right]} $
$4 x-2 y=4$
$ (1) \Rightarrow 2 x-y=2$
$ (2) \Rightarrow 3 x-y=2$
$ -x+y=2$
Add $(1)$ and $(2)$
$2 x-y=2 \cdots(1)$
$\underline{-x+y=2 \cdots(2)}$
$x=4$
Substitute the value of $x=4$ in $(2)$
$-4+y=2$
$ y=2+4=6$
The value of $x = 4$ and $y = 6$
${\left[\begin{array}{c} 4 x \\ -3 x \end{array}\right]+\left[\begin{array}{c} -2 y \\ 3 y \end{array}\right]=\left[\begin{array}{l} 4 \\ 6 \end{array}\right]} $
$4 x-2 y=4$
$ (1) \Rightarrow 2 x-y=2$
$ (2) \Rightarrow 3 x-y=2$
$ -x+y=2$
Add $(1)$ and $(2)$
$2 x-y=2 \cdots(1)$
$\underline{-x+y=2 \cdots(2)}$
$x=4$
Substitute the value of $x=4$ in $(2)$
$-4+y=2$
$ y=2+4=6$
The value of $x = 4$ and $y = 6$
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