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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

      

 

 

 

 

 

Posted by

seema garhwal

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