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If the system of equations
x + y + az = b
2x + 5y + 2z = 6
x + 2y + 3z = 3
has infinitely many solutions, then 2a + 3b is equal to :
- A.
28
- B.
20
- C.
25
- D.
23
(Correct Answer)
Explanation
for infinite many solutions
Δ=Δx=Δy=Δz=0
then Δ=121amp;1amp;5amp;2amp;aamp;2amp;3=0
11−4−a=0⇒a=7
Δz=121amp;1amp;5amp;2amp;bamp;6amp;3=0⇒3−0−b=0⇒b=3
Hence 2a+3b=23
Explanation
for infinite many solutions
Δ=Δx=Δy=Δz=0
then Δ=121amp;1amp;5amp;2amp;aamp;2amp;3=0
11−4−a=0⇒a=7
Δz=121amp;1amp;5amp;2amp;bamp;6amp;3=0⇒3−0−b=0⇒b=3
Hence 2a+3b=23
