If      and      that then:

  • Option 1)

    y=2x

  • Option 2)

    y=-2x

  • Option 3)

    y=x

  • Option 4)

    y=-x

 

Answers (2)

As we learnt in 

Solution of a non-homogeneous system of linear equations by matrix method -

If A is a non-singular matrix then the system of equations given by Ax=b has a unique solution given by x=A^{-1}b

- wherein

 

 A= \begin{bmatrix} 1 &2 &x \\ 3 &-1 &2 \end{bmatrix}

B = \begin{bmatrix} y\\ x\\ 1 \end{bmatrix}

AB= \begin{bmatrix} 6\\ 8 \end{bmatrix}

\therefore \begin{bmatrix} 1 & 2 & x\\ 3 & -1 & 2 \end{bmatrix} \begin{bmatrix} y\\ x\\ 1 \end{bmatrix}= \begin{bmatrix} 6\\ 8 \end{bmatrix}

= \begin{bmatrix} y+ 2x +x\\ 3y- x+ 2 \end{bmatrix}= \begin{bmatrix} 6\\ 8 \end{bmatrix}

\Rightarrow y+3x=6

-x+3y=6

So, y+3x= -x+3y

\Rightarrow 4x = 2y

\therefore y=2x  

 


Option 1)

y=2x

Incorrect

Option 2)

y=-2x

Incorrect

Option 3)

y=x

Correct

Option 4)

y=-x

Incorrect

N neha

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