Solve this


If $x\left[\begin{array}{l}2 \\ 3\end{array}\right]+y\left[\begin{array}{c}-1 \\ 1\end{array}\right]=\left[\begin{array}{c}10 \\ 5\end{array}\right]$, find the value of $x$


$x\left[\begin{array}{l}2 \\ 3\end{array}\right]+y\left[\begin{array}{c}-1 \\ 1\end{array}\right]=\left[\begin{array}{c}10 \\ 5\end{array}\right]$

$\Rightarrow\left[\begin{array}{l}2 x-y \\ 3 x+y\end{array}\right]=\left[\begin{array}{c}10 \\ 5\end{array}\right]$\

Corresponding elements of equal matrices are equal.

$\Rightarrow 2 x-y=10 \quad$ and $\quad 3 x+y=5$

$\Rightarrow y=2 x-10 \quad$ and $\quad 3 x+(2 x-10)=5$

$\Rightarrow y=2 x-10 \quad$ and $\quad 5 x=15$

$\Rightarrow y=2 x-10 \quad$ and $\quad x=3$

$\Rightarrow y=2(3)-10 \quad$ and $\quad x=3$

$\Rightarrow y=-4 \quad$ and $\quad x=3$

$\therefore x=3$ and $y=-4 .$

Hence, the value of $x$ is 3 .


Leave a comment


Click here to get exam-ready with eSaral

For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.

Download Now