QJEEM20Ma64b5: JEE Main 2020 Mathematics - Class 12 JEEM20Ma64b5 Solution: If the system of equations x - 2y + 3z = 9 2x + y + z = b x -…

Question

Verified Solution • 2025–26 Session moderate

If the system of equations
x - 2y + 3z = 9
2x + y + z = b
x - 7y + az = 24,
has infinitely many solutions, then a - b is equal to.........

Accepted Answer

D = 0

| \begin{matrix} 1 & - 2 & 3 \\ 2 & 1 & 1 \\ 1 & - 7 & a \end{matrix} | = 0

1(a + 7) + 2(2a - 1) + 3( - 14 - 1) = 0

a + 7 + 4a - 2 - 45 = 0

5a = 40

a = 8

D_{1} = | \begin{matrix} 9 & - 2 & 3 \\ b & 1 & 1 \\ 24 & - 7 & 8 \end{matrix} | = 0

\Rightarrow 9(8 + 7) + 2(8b - 24) + 3( - 7b - 24) = 0

\Rightarrow 135 + 16b - 48 - 21b - 72 = 0

\Rightarrow

15 = 5b

\Rightarrow b = 3

a - b = 5

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