Given:
The system of equations:
2x + 3y = 6
4x + 6y = 12
To show:
Systems of equations has infinitely many solutions.
Solution:
Consider the equation 2x + 3y = 6
To plot its graph, we have y = \(\frac{6-2x}{3}\)
Putting x = 0 we get y = 2
Putting y = 0 we get x = 3
The table for points of 2x + 3y = 6 is:
Plot A(0, 2) and B(3, 0) in the graph
Consider the equation 4x + 6y = 12
To plot its graph,we have y = \(\frac{12-4x}{6}\)
Putting x = 6 we get y = - 2
Putting y = 4 we get x = - 3
The table for the points 4x + 6y = 12 is:
Plot C(6, - 2) and D(- 3, 4) 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.