Question

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

Answer 1

x$\left[\begin{array}{l}2\\ 3\end{array}\right]$ + y$\left[\begin{array}{l}-1\\ 1\end{array}\right]$ = $\left[\begin{array}{l}10\\ 5\end{array}\right]$.
or $\left[\begin{array}{l}2x\\ 3x\end{array}\right]$ + $\left[\begin{array}{l}-y\\ y\end{array}\right]$ = $\left[\begin{array}{l}10\\ 5\end{array}\right]$
or $\left[\begin{array}{l}2x-y\\ 3x+y\end{array}\right]$ = $\left[\begin{array}{l}10\\ 5\end{array}\right]$
Equating the corresponding elements, we get:
2x – y = 10 … (1)
3x + y = 5 … (2)
Adding (1) and (2), we get
5x – 15 ⇒ x = $\frac{15}{5}$ = 3.
Putting value of x in (1), we get
2x – y = 2 x 3 – y = 10
∴ y = 6 – 10 = – 4.
Hence, x = 3, and y = – 4.