Q. 175.0( 1 Vote )

Find whether the given statement is true or false:

(i) x = 2, y = 3 is a solution of the equation 5x – 3y = 1.

(ii) y = 2x + 5 is a straight line passing through the point (1, 5).

(iii) The area bounded by the line x + y = 6, the x-axis and the y-axis is 18 sq units.

Answer :

(i) Given equation, 5x – 3y = 1


Putting x = 2 and y = 3 in 5x – 3y = 1


LHS = 5x – 3y


= 5× 2 – 3× 3


= 10 – 9


= 1 = RHS


Therefore, the statement is true


(ii) Given equation, y = 2x + 5


Putting x = 1 and y = 5 in y = 2x + 5


y = 2× 1 + 5


y = 2 + 5


y = 7 ≠ 5


Therefore, the statement is false


(iii) Given equation,


x + y = 6


y = 6 – x


When x = 0, then,


y = 6 – x


y = 6 – 0


y = 6


When x = 3, then,


y = 6 – x


y = 6 – 3


y = 3


When x = 6, then,


y = 6 – x


y = 6 – 6


y = 0


Thus we have the following table,



Now on plotting (0, 6), (3, 2) and (6, 0) we have the following graph,


Clearly from the graph,



Base of triangle = 6 – 0 = 6 units


Height of triangle = 6 – 0 = 6 units


We know that, Area of triangle =





= 18 sq. units


Therefore, the area of the triangle is 18 sq. units


Therefore, the statement is true


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