Question

Show graphically that the system of equations 2x + y = 6, 6x + 3y = 20 is inconsistent.

Answer 1

From the first equation, write y in terms of x
y = 6 – 2x …….(i)
Substitute different values of x in (i) to get different values of y
For x = 0, y = 6 – 0 = 6
For x = 2, y = 6 – 4 = 2
For x = 4, y = 6 – 8 = -2
Thus, the table for the first equation (2x + y = 6) is

x	0	2	4
y	6	2	-2

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

y=`(20-6x)/3`                            …….(ii)
Now, substitute different values of x in (ii) to get different values of y

For x = 0, y = `(20 − 0)/3  = 20/3`
For x = `10/3, y = (20 − 20)/3 = 0`
For x = 5, y = `(20 − 30)/3 = −10/3`
So, the table for the second equation (6x + 3y = 20) is

x	0	`10/3`	5
y	`20/3`	0	`-10/3`

Now, plot the points D(0, `20/3`), O(`10/3`, 0) and E(5, −`10/3`) on the same graph paper and join D, E and F to get the graph of 6x + 3y = 20.

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.