The area bounded by the lines x = 0, y = 0, x + y = 1, 2x

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The area bounded by the lines x = 0, y = 0, x + y = 1, 2x + 3y = 6 (in square units) is

1. 2
2. 2 1
  3
3. 2 1
  2
4. 3

Correct Option: C

x = 0 is the equation of y-axis.
y = 0 is the equation of x-axis.
Putting x = 0 in x + y = 1, y = 1
Putting y = 0 in x + y = 1, x = 1
Putting x = 0 in 2x + 3y = 6
3y = 6 ⇒ y = 2
Putting y = 0 in 2x + 3y = 6
2x = 6 ⇒ x = 3
∴ OB = 1; OA = 1
OD = 3; OC = 2
∴ Required area = ∆OCD – ∆OAB

=	1	× 3 × 2 -	1	× 1 × 1
	2		2

= 3 -	1	= 2	1	sq. units
	2		2