(Q.34). Check whether the following equations are consistent or inconsistent. Solve them graphically

2x + y – 6 = 0

4x – 2y – 4 = 0

Given pair of equations 2x + y – 6 = 0 and 4x – 2y – 4 = 0

a1
a2
 =
=
;
b1
b2
 =
1
-
 =
-1
;
c1
c2
 =
-
-
 =
∴
a1
a2
 ≠
b1
b2

The equations are consistent.

∴ They intersect at one point giving only one solution.

2x + y = 6
x y (x,y)
0 (0,)
3 (3,)
4x - 2y = 4
x y (x,y)
0 - (0,-)
1 (1,)

The solution is x = and y =