Q. On comparing the ratios
a1
a2
,
b1
b2
and
c1
c2
, find out whether
the lines representing the following pairs of linear equations
are Consistent, or inconsistent:
Soln.
5x
–
3y
=
11
–10x
+
6y
=
– 22
... (i)
... (ii)
Comparing equation
(i)
with
a1x
+
b1y
+
c1
=
0
and equation (ii) with
a2x
+
b2y
+
c2
=
0
We get
a1
=
5
a2
=
–10
b1
=
–3
b2
=
6
c1
=
–11
c2
=
22
5x
–
3y
11 = 0
–10x
+
6y
a1
a2
5
–10
=
b1
b2
–3
6
=
c1
c2
–11
22
=
... (iii)
... (iv)
... (v)
–1
2
=
–1
2
=
from (iii), (iv) and (v)
a1
a2
b1
b2
=
The pair of linear equations
are consistent.
–
+ 22
= 0
Equations has no solution(Inconsistent)
Equations has infinite solutions(Consistent)
Intersecting lines
Parallel lines
Coincident line
Equations has unique solution (Consistent)
–1
2
=
c1
c2
=
To get this, the equations has to be in standard form
Q. On comparing the ratios
a1
a2
,
b1
b2
and
c1
c2
, find out whether
the lines representing the following pairs of linear equations
are Consistent, or inconsistent:
Soln.
x
+
2y
= 8
2x
+
3y
= 12
... (i)
... (ii)
Comparing equation
(i)
with
a1x
+
b1y
+
c1
=
0
and equation (ii) with
a2x
+
b2y
+
c2
=
0
We get
a1
=
a2
=
2
b1
=
2
b2
=
3
c1
=
–8
c2
=
–12
x
+ 2y
=
– 8
2x
+
3y
=
0
a1
a2
2
=
b1
b2
2
3
=
c1
c2
–8
–12
=
... (iii)
... (iv)
... (v)
8
12
=
from (iii), (iv) and (v)
a1
a2
b1
b2
=
The pair of linear equations are consistent.
0
12
–
Equations has no solution(Inconsistent)
Equations has infinite solutions(Consistent)
To get this the equations has to be in standard form
Intersecting lines
Parallel lines
Coincident line
Equations has unique solution (Consistent)
4
3
4
3
4
3
4
3
4
6
=
2
3
=
2
3
=
c1
c2
=