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If and that then:

Option 1)
$y=2x$

Option 2)
$y=-2x$

Option 3)
$y=x$

Option 4)
$y=-x$

Answers (2)

best_answer

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

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Aadil

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