Q. 335.0( 1 Vote )

Show that (3, 1) as well as (2, – 2) are the solutions of the equation 3x – y = 8. Find two more solutions. How many solutions can we find?

Answer :

The equation is 3x – y = 8


For (3, 1), x = 3 and y = 1


LHS = 3×3 – 1


= 9 – 1


= 8 = RHS


Since, RHS = LHS, therefore, (3, 1) is the solution of the equation 3x – y = 8.


For (2, – 2), x = 2 and y = – 2


LHS = 3×3 – 1


= 9 – 1


= 8 = RHS


Since, RHS = LHS, therefore, (2, – 2) is the solution of the equation 3x – y = 8.


Hence, (3, 1) and (2, – 2) are the solutions of the equation 3x – y = 8.


Now to find two more solutions,


3x – y = 8


y = 3x – 8


Let x = 1, then, y = 3x – 8


y = 3×1 – 8


y = 3 – 8


y = – 5


Therefore, (1, – 5) is a solution of 3x – y = 8.


Let x = 4, then, y = 3x – 8


y = 3×4 – 8


y = 12 – 8


y = 4


Therefore, (4, 4) is a solution of 3x – y = 8.


Plotting the points we obtain the following graph,



The blue line in the graph is of the equation 3x – y = 8.


From the graph, it is clear that it has infinitely many solutions.


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