Question

If x $\begin{bmatrix}2\\\3\end{bmatrix}$+y $\begin{bmatrix}-1\\\1\end{bmatrix}$=$\begin{bmatrix}10\\\5\end{bmatrix}$,find values of x and y.

Answer 1

x $\begin{bmatrix}2\\\3\end{bmatrix}$+y $\begin{bmatrix}-1\\\1\end{bmatrix}$=$\begin{bmatrix}10\\\5\end{bmatrix}$

$\Rightarrow \begin{bmatrix}2x\\\3x\end{bmatrix}+\begin{bmatrix}-y\\\y\end{bmatrix}$=$\begin{bmatrix}10\\\5\end{bmatrix}$

$\Rightarrow \begin{bmatrix}2x-y\\\3x+y\end{bmatrix}$=$\begin{bmatrix}10\\\5\end{bmatrix}$

Comparing the corresponding elements of these two matrices, we get:
2x − y = 10 and 3x + y = 5
Adding these two equations, we have:
5x = 15
$\Rightarrow$ x = 3
Now, 3x + y = 5
$\Rightarrow$ y = 5 − 3x
$\Rightarrow$ y = 5 − 9 = −4

∴x = 3 and y = −4