Question

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

Show graphically that the following given system of equations is inconsistent, i.e., has no solution:

x – 2y = 6, 3x – 6y = 0

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.