Question

To solve simultaneous equations x + 2y = 4; 3x + 6y = 12 graphically, following are the ordered pairs.

Plotting the above ordered pairs, graph is drawn. Observe it and find answers of the following questions.

i. Are the graphs of both the equations different or same? 

ii. What are the solutions of the two equations x + 2y = 4 and 3x + 6y = 12? How many solutions are possible? 

iii. What are the relations between coefficients of x, coefficients of y and constant terms in both the equations? 

iv. What conclusion can you draw when two equations are given but the graph is only one line?

Answer 1

i. The graphs of both the equations are same. 

ii. The solutions of the given equations are (-2, 3), (0, 2), (1, 1.5), etc. 

∴ Infinite solutions are possible.

iii. Ratio of coefficients of x = 1/3

Ratio of coefficients of y = 2/6 = 1/3

Ratio of constant terms = 4/12 = 1/3

∴ Ratios of coefficients of x = ratio of coefficients of 

y = ratio of the constant terms 

iv. When two equations are given but the graph is only one line, the equations will have infinite solutions.