AP EAMCET Engineering 20 Apr 2019 Shift 1 Paper

Consider the system of equations,
2x+3|y|+5[z]=0
x+|y|−2[z]=4
x+|y|+[z]=1
Then by Cramer's rule,
x=‌‌

∆1

∆

|y|=‌‌

∆2

∆

[z]=‌‌

∆3

∆

Where
∆=|

2	3	5
1	1	−2
1	1	1

|
=2(1+2)−3(1+2)+5(1−1)
=−3
and
∆1=|

0	3	5
4	1	−2
1	1	1

|
=0(1+2)−3(4+2)+5(4−1)
=−3 and
∆2=|

2	0	5
1	4	−2
1	1	1

|
=2(4+2)−0(1+2)+5(1−4)
=−3
and,
∆3=|

2	3	0
1	1	4
1	1	1

|
=2(1−4)−3(1−4)+0(1−1)
=3
This implies
x=‌‌

−3

−3

=1
And
|y|=‌‌

−3

−3

=1
And
[z]=‌‌

−3

3

=−1
This implies,
z∈[−1,0)
So, the system has infinitely many solutions.