The system of equations alpha x+y+z=alpha-1x+alpha y+z=alpha--Turito

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Maths-

General

Easy

Question

The system of equations $alpha x plus y plus z equals alpha minus 1 x plus alpha y plus z equals alpha minus 1 x plus y plus alpha z equals alpha minus 1$ has no solution, if $alpha$ is

Not – 2
1
– 2
Either – 2 or 1

The correct answer is: – 2

For no solution or infinitely many solutions $open vertical bar table row alpha 1 1 row 1 alpha 1 row 1 1 alpha end table close vertical bar equals 0 rightwards double arrow alpha equals 1 comma alpha equals negative 2$ .
But for $alpha equals 1$ , clearly there are infinitely many solutions and when we put $alpha equals negative 2$ in given system of equations and adding them together L.H.S $not equal to$ R.H.S. i.e., No solution.

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