Question

Show graphically that the system of equations x - 2y = 6, 3x - 6y = 0 is inconsistent.

Answer 1

From the first equation, write y in terms of x
y =` (x −6)/2`                                      …….(i)
Substitute different values of x in (i) to get different values of y

For x = -2, y =`(-2-6)/2 = -4`

For x = 0, y = `(0 − 6)/2= -3`
For x = 2, y = `(2 − 6)/2 = -2`

Thus, the table for the first equation (x - 2y = 5) is

x	-2	0	2
y	-4	-3	-2

Now, plot the points A(-2, -4), B(0, -3) and C(2, -2) on a graph paper and join A, B and C to get the graph of x - 2y = 6.
From the second equation, write y in terms of x

y`=1/2`x                            …….(ii)
Now, substitute different values of x in (ii) to get different values of y

For x = -4, y = `−4/2 = -2`
For x = 0, y = `0/2 = 0`
For x = 4, y =` 4/2 = 2`
So, the table for the second equation (3x - 6y = 0) is

x	-4	0	4
y	-2	0	2

Now, plot the points D(-4, -2), O(0, 0) and E(4, 2) on the same graph paper and join D, E and F to get the graph of 3x - 6y = 0.

From the graph, it is clear that, the given lines do not intersect at all when produced.  Hence, the system of equations has no solution and therefore is inconsistent.