For the system of linear equations x+y+z=6 \alpha x+\beta y+7 z=3 x+2 y+3 z=14 which of the following is NOT true? [31-Jan-2023 Shift 1]

Correct Answer is : For every point (α,β)≠(7,7) on the line x−2y+7=0, the system has infinitely many solutions.

If \alpha=\beta=7, then the system has no solution

If \alpha=\beta and \alpha \neq 7 then the system has a unique solution.

There is a unique point (\alpha, \beta) on the line x+2 y+18=0 for which the system has infinitely many solutions

For every point (\alpha, \beta) \neq(7,7) on the line {\x}-2 {\y}+7=0, the system has infinitely many solutions.

JEE Mains 31-Jan-2023 Shift 1 Solved Paper

Section: Mathematics

Question : 64 of 90

Marks: +1, -0

For the system of linear equations
‌x+y+z=6
‌αx+βy+7z=3
‌x+2y+3z=14
which of the following is NOT true?

[31-Jan-2023 Shift 1]

If α=β=7, then the system has no solution
If α=β and α≠7 then the system has a unique solution.
There is a unique point (α,β) on the line x+2y+18=0 for which the system has infinitely many solutions
For every point (α,β)≠(7,7) on the line x−2y+7=0, the system has infinitely many solutions.

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