JEE Main 202331 Jan, Morning shiftMathematicsEasyMatrices and Determinants245× since 2002For the system of linear equations x+y+z=6x+y+z=6x+y+z=6 αx+βy+7z=3\alpha x+\beta y+7 z=3αx+βy+7z=3 x+2y+3z=14x+2 y+3 z=14x+2y+3z=14 which of the following is NOT true ?AOption A. If α=β=7\alpha=\beta=7α=β=7, then the system has no solutionBOption B. For every point (α,β)≠(7,7)(\alpha, \beta) \neq(7,7)(α,β)=(7,7) on the line x−2y+7=0x-2 y+7=0x−2y+7=0, the system has infinitely many solutionsCOption C. There is a unique point (α,β)(\alpha, \beta)(α,β) on the line x+2y+18=0x+2 y+18=0x+2y+18=0 for which the system has infinitely many solutionsDOption D. If α=β\alpha=\betaα=β and α≠7\alpha \neq 7α=7, then the system has a unique solutionCheckSkip · show solution
