Question

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

3x + y = 8

6x + 2y = 16

Answer 1

Given:

The system of equations:

3x + y = 8

6x + 2y = 16

To show:

Systems of equations has infinitely many solutions.

Solution:

Consider the equation 3x+y = 8

To plot its graph,we have y=8 - 3x

Putting x = 0 we get y = 8

Putting y = 2 we get x = 2

The table for points of 3x+y = 8 is:

x	0	2
y	8	2

Plot A(0,8) and B(2,2) in the graph

Consider the equation 6x+2y = 16

To plot its graph,we have

y = \(\frac{16-2x}{6}\)

Putting x=2 we get y=2

Putting y=0 we get x=8

The table for the points 6x+2y = 16 is:

x	1	3
y	5	-1

Plot C(1,5) and D(3,-1) in the graph

Now plot the graphs for these equations as:

As Both the lines pass through the same points and are coinciding.

There can be infinite points lying on both the lines.

Hence,systems of equations has infinitely many solutions.