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Find the area enclosed by the common region of |x + 2| + |y+ 2| = 2 and 2x - 3y > 6 
  • a)
    7.2 sq.units
  • b)
    2.4 sq.units
  • c)
    1.2 sq. units
  • d)
    None of the above
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
Find the area enclosed by the common region of |x + 2| + |y+ 2| = 2 an...
The common region will be the Δ DEC as shown below,

Now, D = (0, -2); C e (-2, -4)
The third co-ordinate E can be found by solving the equations, 2x - 3y = 6 & x + y = -6
E = (-12/5, -18/5)
Now we know that

Substituting the three co-ordinates, we get,
A(ΔEFC) = 0.8 sq. units
Hence, option 4.
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Most Upvoted Answer
Find the area enclosed by the common region of |x + 2| + |y+ 2| = 2 an...
Given equations:
|x + 2| + |y + 2| = 2
2x - 3y = 6

Finding the intersection points:
1. Let's first find the intersection points of the two equations.
2. Substitute y = (2x - 6)/3 into the first equation.
3. |x + 2| + |(2x - 6)/3 + 2| = 2
4. Solve for x to find the x-coordinates of the intersection points.

Calculating the area enclosed:
1. The area enclosed by the common region is the area between the curves and the x-axis.
2. Calculate the integral of the function for the x-values of the intersection points to find the area enclosed.
3. The integral of |x + 2| + |y + 2| = 2 represents the area between the curve and the x-axis.

Final answer:
The area enclosed by the common region of the two curves is not a simple geometric shape, so it cannot be directly calculated. The correct answer is option 'D' - None of the above.
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Find the area enclosed by the common region of |x + 2| + |y+ 2| = 2 and 2x - 3y 6a)7.2 sq.unitsb)2.4 sq.unitsc)1.2 sq. unitsd)None of the aboveCorrect answer is option 'D'. Can you explain this answer?
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