prove that following system of linear equations has infinite number of solutions

Question : Prove that following system of linear equations has infinite number of solutions3x-y+2z=49x-7y+z=-2Solution :Given system of linear equations 3x-y+2z=4 (1) 9x-7y+z=-2 (2) Writing equations (1) and (2) in matrix form AX=B \[\left(\begin{matrix}3&-1&2\\9&-7&1\end{matrix}\right)\left(\begin{matrix}x\\y\\z\end{matrix}\right)=\left(\begin{matrix}4\\-2\end{matrix}\right) \] (3) Augmented matrix is \[\left[A:B\right]=\left(\begin{matrix}3&-1&2&4\\9&-7&1&-2\end{matrix}\right)\] Applying…

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