Question

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

$2x+y=6,6x+3y=18.$

Answer 1

Given equations are 2x + y = 6 and 6x + 3y = 18

Graph of 2x + y = 6:

2x + y = 6

⇒y = −2x + 6

Putting x = 3, we get y = 0

Putting x = 1, we get y = 4

Putting x = 2, we get y = 2

Hence, the table is,

X	3	1	2
Y	0	4	2

Plot the points A(3, 0), B(1, 4) and C(2, 2) on the graph paper. Join AC and BC to get the graph line of equation 2x + y = 6.

Graph of 6x + 3y = 18:

6x + 3y = 18
⇒ $y=\frac{(-6x+18)}{3}$

Putting x = 0, we get y = -5

Putting x = 1, we get y = -2

Putting x = 2, we get y = 1

Hence, the table is:

X	3	1	2
Y	0	4	2

These points are same as obtained above:

Thus, we find that the two line graphs coincide. Hence, the given system of equations has infinitely many solutions