Question

Show graphically that each one of the following systems of equations has infinitely many solutions:
x – 2y = 5
3x – 6y = 15

Answer 1

Two lines overlap each other

Step-by-step explanation:

Given linear equations are  

x – 2y = 5---- (1)

3x – 6y = 15 ---- (2)

Co-ordinates for equation 1 will be (5, 0), (7 , 1), (9, 4), (15, 5)

Co-ordinates for equation 2 will be (5, 0), (7 , 1), (9, 4), (15, 5)

We find that the two lines when plotted will overlap each other on the graph. So there are infinite number of points of intersections of the two lines. Hence they have has infinitely many solutions.

Answer 2

Given linear equations are  

x – 2y = 5---- (1)

3x – 6y = 15 ---- (2)

Co-ordinates for equation 1 will be (5, 0), (7 , 1), (9, 4), (15, 5)

Co-ordinates for equation 2 will be (5, 0), (7 , 1), (9, 4), (15, 5)

We find that the two lines when plotted will overlap each other on the graph. So there are infinite number of points of intersections of the two lines. Hence they have has infinitely many solutions.