AP EAMCET Engineering 22 Apr 2019 Shift 1 Paper

Consider the system of equation,
x+y+z=a …… (1)
x−y+bz=2 …… (2)
2x+3y−z=1 …… (3)
As these equations have infinitely many solutions, therefore,
[

1	1	1
1	−1	b
2	3	−1

]=0
1(1−3b)−1(−1−2b)+1(3+2)=0
−b=−7
b=7
From equation (1) and (2),
2x+8z=a+2
x+4z=

a+2

2

…… (4)
From equation (1) and (3), we get
x+4x=3a−1 …… (5)
From equation (4) and (5), we get

a+2

2

=3a−1
a+2=6a−2
5a=4
So, the required value is,
b−5a=7−4
=3