MCQ
If $x\left[\begin{array}{r}-1 \\ 2\end{array}\right]+4\left[\begin{array}{r}2 \\ -y\end{array}\right]-\left[\begin{array}{r}7 \\ -8\end{array}\right]$, then the respective values of $x$ and $y$ are:
  • A
    $-1, \frac{3}{2}$
  • B
    $15, \frac{19}{2}$
  • $1, \frac{5}{2}$
  • D
    $-1, \frac{5}{2}$

Answer

Correct option: C.
$1, \frac{5}{2}$
(c) $1, \frac{5}{2}$
Explanation:
$\begin{array}{l}x\left[\begin{array}{r}-1 \\ 2\end{array}\right]+4\left[\begin{array}{r}2 \\ -y\end{array}\right]=\left[\begin{array}{r}7 \\ -8\end{array}\right] \\ \Rightarrow\left[\begin{array}{r}-x \\ 2
x\end{array}\right]+\left[\begin{array}{c}8 \\ -4 y\end{array}\right]=\left[\begin{array}{r}7 \\ -8\end{array}\right] \\ \Rightarrow\left[\begin{array}{r}-x+8 \\ 2 x-4 y\end{array}\right]=\left[\begin{array}{r}7 \\ -8\end{array}\right] \\ \Rightarrow-x+8=7\end{array}$
and $2 x-4 y=-8$
$\begin{array}{l}\Rightarrow-x=-1 \\ \Rightarrow x=1\end{array}$
So, $2(1)-4 y=-8$
$\begin{array}{l}\Rightarrow-4 y=-10 \\ \Rightarrow y=\frac{5}{2}\end{array}$

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