Q. Which of the following pairs of linear equations are consistent/inconsistent?
If consistent, obtain the solution graphically:
Soln.
2x
+
y
–
6
4x
+
2y
–
4
... (i)
... (ii)
Comparing equation
(i)
with
a1x
+
b1y
+
c1
=
0
and equation (ii) with
a2x
+
b2y
+
c2
=
0
a1
=
2
a2
=
4
b1
=
1
b2
=
– 2
c1
=
– 6
c2
=
– 4
2 x
+
y
=
6
4 x
–
2 y
=
0
a1
a2
2
4
=
b1
b2
1
– 2
=
c1
c2
– 6
– 4
=
... (iii)
... (iv)
... (v)
3
2
=
–
0
4
–
From (iii), (iv) and (v)
a1
a2
≠
b1
b2
2x + y – 6 = 0
x
y
(x, y)
0
6
(0, 6)
3
0
(3, 0)
x
y
(x, y)
2
2
(2, 2)
1
0
(1, 0)
4x – 2y – 4 = 0
=
0
=
0
1
2
=
Now to represent graphically,
we find two solutions of each
equation
Scale
1 cm = 1 unit on both the axes
Y
X
X
Y
0
1
3
2
5
4
6
1
2
3
4
5
6
(0 , 6)
(3 ,0)
2x + y – 6 = 0
(2,2)
(1 , 0)
4x + 2y – 4 = 0
∴
(2, 2) is the common solution for both the equation.
1
≠
c1
c2