1
You visited us
1
times! Enjoying our articles?
Unlock Full Access!
Byju's Answer
Standard X
Mathematics
Graphical Method of Finding Solution of a Pair of Linear Equations
Show that eac...
Question
Show that each one of the following systems of linear equation is inconsistent:
(i) 2x + 5y = 7
6x + 15y = 13
(ii) 2x + 3y = 5
6x + 9y = 10
(iii) 4x − 2y = 3
6x − 3y = 5
(iv) 4x − 5y − 2z = 2
5x − 4y + 2z = −2
2x + 2y + 8z = −1
(v) 3x − y − 2z = 2
2y − z = −1
3x − 5y = 3
(vi) x + y − 2z = 5
x − 2y + z = −2
−2x + y + z = 4
Open in App
Solution
(i) The given system of equations can be expressed as follows:
A
X
=
B
Here
,
A
=
2
5
6
15
,
X
=
x
y
and
B
=
7
13
Now
,
A
=
2
5
6
15
=
30
-
30
=
0
Let C
i
j
be the cofactors of the elements a
i
j
in A =
a
i
j
. Then,
C
11
=
-
1
1
+
1
15
=
15
,
C
12
=
-
1
1
+
2
6
=
-
6
C
21
=
-
1
2
+
1
5
=
-
5
,
C
22
=
-
1
2
+
2
2
=
2
adj
A
=
15
-
6
-
5
2
T
=
15
-
5
-
6
2
adj
A
B
=
15
-
5
-
6
2
7
13
=
105
-
65
-
42
+
26
=
40
-
16
≠
0
Hence, the given system of equations is inconsistent.
(ii) The given system of equations can be expressed as follows:
A
X
=
B
Here
,
A
=
2
3
6
9
,
X
=
x
y
and
B
=
5
10
Now
,
A
=
2
3
6
9
=
18
-
18
=
0
Let C
i
j
be the cofactors of the elements a
i
j
in A =
a
i
j
. Then,
C
11
=
-
1
1
+
1
9
=
9
,
C
12
=
-
1
1
+
2
6
=
-
6
C
21
=
-
1
2
+
1
3
=
-
3
,
C
22
=
-
1
2
+
2
2
=
2
adj
A
=
9
-
6
-
3
2
T
=
9
-
3
-
6
2
adj
A
B
=
9
-
3
-
6
2
5
10
=
45
-
30
-
30
+
20
=
15
-
10
≠
0
Hence, the given system of equations is inconsistent.
(iii) The given system of equations can be expressed as follows:
A
X
=
B
Here
,
A
=
4
-
2
6
-
3
,
X
=
x
y
and
B
=
3
5
A
=
4
-
2
6
-
3
=
-
12
+
12
=
0
Let C
i
j
be the cofactors of the elements a
i
j
in A =
a
i
j
. Then,
C
11
=
-
1
1
+
1
-
3
=
-
3
,
C
12
=
-
1
1
+
2
6
=
-
6
C
21
=
-
1
2
+
1
-
2
=
2
,
C
22
=
-
1
2
+
2
4
=
4
adj
A
=
-
3
-
6
2
4
T
=
-
3
2
-
6
4
a
d
j
A
B
=
-
3
2
-
6
4
3
5
=
-
9
+
10
-
18
+
20
=
1
2
≠
0
Hence, the given system of equations is inconsistent.
(iv) The given system of equations can be written as follows:
A
X
=
B
Here
,
A
=
4
-
5
-
2
5
-
4
2
2
2
8
,
X
=
x
y
z
and
B
=
2
-
2
-
1
A
=
4
-
5
-
2
5
-
4
2
2
2
8
=
4
-
32
-
4
+
5
40
-
4
-
2
(
10
+
8
)
=
-
144
+
180
-
36
=
0
Let C
i
j
be the cofactors of the elements a
i
j
in A
a
i
j
. Then,
C
11
=
-
1
1
+
1
-
4
2
2
8
=
28
,
C
12
=
-
1
1
+
2
5
2
2
8
=
-
36
,
C
13
=
-
1
1
+
3
5
-
4
2
2
=
18
C
21
=
-
1
2
+
1
-
5
-
2
2
8
=
36
,
C
22
=
-
1
2
+
2
4
-
2
2
8
=
36
,
C
23
=
-
1
2
+
3
4
-
5
2
2
=
-
18
C
31
=
-
1
3
+
1
-
5
-
2
-
4
2
=
-
18
,
C
32
=
-
1
3
+
2
4
-
2
5
2
=
-
18
,
C
33
=
-
1
3
+
3
4
-
5
5
-
4
=
9
adj
A
=
28
-
36
18
36
36
-
18
-
18
-
18
9
T
=
28
36
-
18
-
36
36
-
18
18
-
18
9
adj
A
B
=
28
36
-
18
-
36
36
-
18
18
-
18
9
2
-
2
-
1
=
56
-
72
+
18
-
72
-
72
+
18
36
+
36
-
9
=
2
-
126
63
≠
0
Hence, the given system of equations is consistent.
(v) The given system of equations can be written as follows:
A
X
=
B
Here
,
A
=
3
-
1
-
2
0
2
-
1
3
-
5
0
,
X
=
x
y
z
and
B
=
2
-
1
3
A
=
3
-
1
-
2
0
2
-
1
3
-
5
0
=
3
0
-
5
+
1
0
+
3
-
2
(
0
-
6
)
=
-
15
+
3
+
12
=
0
Let C
i
j
be the cofactors of the elements a
i
j
in A
a
i
j
. Then,
C
11
=
-
1
1
+
1
2
-
1
-
5
0
=
-
5
,
C
12
=
-
1
1
+
2
0
-
1
3
0
=
-
3
,
C
13
=
-
1
1
+
3
0
2
3
-
5
=
-
6
C
21
=
-
1
2
+
1
-
1
-
2
-
5
0
=
10
,
C
22
=
-
1
2
+
2
3
-
2
3
0
=
6
,
C
23
=
-
1
2
+
3
3
-
1
3
-
5
=
12
C
31
=
-
1
3
+
1
-
1
-
2
2
-
1
=
5
,
C
32
=
-
1
3
+
2
3
-
2
0
-
1
=
3
,
C
33
=
-
1
3
+
3
3
-
1
0
2
=
6
adj
A
=
-
5
-
3
-
6
10
6
12
5
3
6
T
=
-
5
10
5
-
3
6
3
-
6
12
6
adj
A
B
=
-
5
10
5
-
3
6
3
-
6
12
6
2
-
1
3
=
-
10
-
10
+
15
-
6
-
6
+
9
-
12
-
12
+
18
=
-
5
-
3
-
6
≠
0
Hence, the given system of equations is consistent.
(vi) The given system of equations can be written as follows:
A
X
=
B
Here
,
A
=
1
1
-
2
1
-
2
1
-
2
1
1
,
X
=
x
y
z
and
B
=
5
-
2
4
A
=
1
1
-
2
1
-
2
1
-
2
1
1
=
1
-
2
-
1
-
1
1
+
2
-
2
(
1
-
4
)
=
-
3
-
3
+
6
=
0
Let C
i
j
be the cofactors of the elements a
i
j
in A
a
i
j
. Then,
C
11
=
-
1
1
+
1
-
2
1
1
1
=
-
3
,
C
12
=
-
1
1
+
2
1
1
-
2
1
=
-
3
,
C
13
=
-
1
1
+
3
1
-
2
-
2
1
=
-
3
C
21
=
-
1
2
+
1
1
-
2
1
1
=
-
3
,
C
22
=
-
1
2
+
2
1
-
2
-
2
1
=
-
3
,
C
23
=
-
1
2
+
3
1
1
-
2
1
=
-
3
C
31
=
-
1
3
+
1
1
-
2
-
2
1
=
-
3
,
C
32
=
-
1
3
+
2
1
-
2
1
1
=
-
3
,
C
33
=
-
1
3
+
3
1
1
1
-
2
=
-
3
adj
A
=
-
3
-
3
-
3
-
3
-
3
-
3
-
3
-
3
-
3
T
=
-
3
-
3
-
3
-
3
-
3
-
3
-
3
-
3
-
3
adj
A
B
=
-
3
-
3
-
3
-
3
-
3
-
3
-
3
-
3
-
3
5
-
2
4
=
-
15
+
6
-
12
-
15
+
6
-
12
-
15
+
6
-
12
=
-
21
-
21
-
21
≠
0
Hence, the given system of equations is consistent.
Suggest Corrections
0
Similar questions
Q.
Show that each one of the following systems of linear equation is inconsistent:
(i) 2x + 5y = 7
6x + 15y = 13
(ii) 2x + 3y = 5
6x + 9y = 10
(iii) 4x − 2y = 3
6x − 3y = 5
(iv) 4x − 5y − 2z = 2
5x − 4y + 2z = −2
2x + 2y + 8z = −1
(v) 3x − y − 2z = 2
2y − z = −1
3x − 5y = 3
(vi) x + y − 2z = 5
x − 2y + z = −2
−2x + y + z = 4
Q.
Show that each of the following systems of linear equations is consistent and also find their solutions:
(i) 6x + 4y = 2
9x + 6y = 3
(ii) 2x + 3y = 5
6x + 9y = 15
(iii) 5x + 3y + 7z = 4
3x + 26y + 2z = 9
7x + 2y + 10z = 5
(iv) x − y + z = 3
2x + y − z = 2
−x −2y + 2z = 1
(v) x + y + z = 6
x + 2y + 3z = 14
x + 4y + 7z = 30
(vi) 2x + 2y − 2z = 1
4x + 4y − z = 2
6x + 6y + 2z = 3
Q.
2x + y − 2z = 4
x − 2y + z = − 2
5x − 5y + z = − 2
Q.
Solve the following systems of equations.
x
+
2
y
−
z
=
7
,
2
x
−
y
+
z
=
2
,
3
x
−
5
y
+
2
z
=
−
7
Q.
Solve:
2
x
−
3
y
+
4
z
=
0
7
x
+
2
y
−
6
z
=
0
4
x
+
3
y
+
z
=
37
View More
Join BYJU'S Learning Program
Grade/Exam
1st Grade
2nd Grade
3rd Grade
4th Grade
5th Grade
6th grade
7th grade
8th Grade
9th Grade
10th Grade
11th Grade
12th Grade
Submit
Related Videos
Graphical Solution
MATHEMATICS
Watch in App
Explore more
Graphical Method of Finding Solution of a Pair of Linear Equations
Standard X Mathematics
Join BYJU'S Learning Program
Grade/Exam
1st Grade
2nd Grade
3rd Grade
4th Grade
5th Grade
6th grade
7th grade
8th Grade
9th Grade
10th Grade
11th Grade
12th Grade
Submit
AI Tutor
Textbooks
Question Papers
Install app
