If x 2 3 +y -1 1 = 10 5 , find the values of x and y. - Vidyadip

Question

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

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Answer

Given: $x\begin{bmatrix}2\\3\end{bmatrix}+y\begin{bmatrix}-1\\1\end{bmatrix}=\begin{bmatrix}10\\5\end{bmatrix}$
$\Rightarrow\begin{bmatrix}2x\\3x\end{bmatrix}+\begin{bmatrix}-y\\ y\end{bmatrix}=\begin{bmatrix}10\\5\end{bmatrix}$
$\Rightarrow \begin{bmatrix}2x-y\\3x+y\end{bmatrix}=\begin{bmatrix}10\\5\end{bmatrix}$
Equating corresponding entries, we have
2x - y = 10 ...(i)
3x + y = 5 ...(ii)
Adding eq. (i) and (ii), we have 5x = 15 ⇒ x = 3
Putting x = 3 in eq. (ii), 9 + y = 5 ⇒ y = -4

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