Question

Show graphically that the system of equations x – 2y = 5, 3x – 6y = 15 has infinitely many solutions.

Show graphically that the following given system of equations has infinitely many solutions:

x – 2y = 5, 3x – 6y = 15

Answer 1

From the first equation, write y in terms of x 

`y = (x - 5)/2`   ...(i)

Substitute different values of x in (i) to get different values of y

For x = –5, y = `(-5 - 5)/2` = –5

For x = 1, y = `(1 - 5)/2` = –2

For x = 3, y = `(3 - 5)/2` = –1

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

x	–5	1	3
y	–5	–2	–1

Now, plot the points A(–5, –5), B(1, –2) and C(3, –1) on a graph paper and join A, B and C to get the graph of x – 2y = 5.

From the second equation, write y in terms of x

`y = (3x - 15)/6`   ...(ii)

Now, substitute different values of x in (ii) to get different values of y

For x = –3, y = `(-9 - 15 )/6` = –4

For x = –1, y = `(-3 - 15)/6` = –3

For x = 5, y = `(15 - 15)/6` = 0

So, the table for the second equation (3x – 6y = 15) is

x	–3	–1	5
y	–4	–3	0

Now, plot the points D(–3, –4), E(–1, –3) and F(5, 0) on the same graph paper and join D, E and F to get the graph of 3x – 6y = 15.

From the graph, it is clear that, the given lines coincide with each other.

Hence, the solution of the given system of equations has infinitely many solutions.