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

Q11.    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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$x\begin{bmatrix}2\\3 \end{bmatrix} + y\begin{bmatrix} -1\\1 \end{bmatrix} = \begin{bmatrix} 10\\5 \end{bmatrix}$

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

Adding both the matrix in LHS and rewriting

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

$2x-y=10........................1$

$3x+y=5........................2$

Adding equation 1 and 2, we get

$5x=15$

$x=3$

Put the value of x in equation 2, we have

$3x+y=5$

$3\times 3+y=5$

$9+y=5$

$y=5-9$

$y=-4$

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