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Mathematics
Mathematics
Problem
If the system of linear equations
3
x
+
y
+
β
z
=
3
3x + y + \beta z = 3
3
x
+
y
+
β
z
=
3
2
x
+
α
y
−
z
=
−
3
2x + \alpha y - z = -3
2
x
+
α
y
−
z
=
−
3
x
+
2
y
+
z
=
4
x + 2y + z = 4
x
+
2
y
+
z
=
4
has infinitely many solutions, then the value of
22
β
−
9
α
22\beta - 9\alpha
22
β
−
9
α
is : (1) 49 (2) 31 (3) 43 (4) 37
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