Total number of solutions to the system of linear equations $x + y + z = 1, 2 x + 2 y + 2 z = 3,$
$x + y = 1$ is infinity.

True

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False

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Solution

The correct option is B
False

Once you express the given equations in the form of matrices the determinant $D = 0, D_{1} = 1, D_{2} = - 1, D_{3} = 0$ . Therefore $D = 0$ and not all of $D_{1}, D_{2}, D_{3}$ are 0. So according to Cramer's rule there exists no solutions at all.

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