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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