If the system of linear equations 3 x + y + β z = 3 2 x + α y − z = − 3 x + 2 y + z = 4 has infinitely many solutions, then the value of 22 β − 9 α is :

Question

If the system of linear equations ​ 3 x + y + β z = 3 2 x + α y − z = − 3 x + 2 y + z = 4 ​ has infinitely many solutions, then the value of 22 β − 9 α is :

TestHub · Accepted Answer

Δ = ​ 3 2 1 ​ 1 α 2 ​ β − 1 1 ​ ​ = 0 3 α + 4 β − α β + 3 = 0 Δ 3 ​ = ​ 3 2 1 ​ 1 α 2 ​ 3 − 3 4 ​ ​ = 0 9 α + 19 = 0 α = 9 − 19 ​ , β = 11 6 ​ ⇒ 22 β − 9 α = 31

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