Question

If $x\left[ \begin{matrix} -3 \\\ 4 \\\ \end{matrix} \right]+y\left[ \begin{matrix} 4 \\\ 3 \\\ \end{matrix} \right]=\left[ \begin{matrix} 10 \\\ -5 \\\ \end{matrix} \right],$ then

• A. $x=-2,\,y=1$
• B. $x=-9,y=10$
• C. $x=22,y=1$
• D. $x=2,y=-1$

Answer 1

Answer: (A)

$x=-2,\,y=1$

Answer 2

Given that, $x\left[ \begin{matrix} -3 \\\ 4 \\\ \end{matrix} \right]+y\left[ \begin{matrix} 4 \\\ 3 \\\ \end{matrix} \right]=\left[ \begin{matrix} 10 \\\ -5 \\\ \end{matrix} \right]$
$\therefore$ $-3x+4y=10$ ..(i)
and $4x+3y=-5$ ..(ii)
On multiplying E (i) by 4 and E (ii) by 4 and then subtracting, we get
$-25x=50$
$\Rightarrow$ $x=-2$