4,853 views
13 votes
13 votes

Find the area bounded by the lines $3x + 2y=14, 2x - 3y = 5$ in the first quadrant.

  1. $14.95$
  2. $15.25$
  3. $15.70$
  4. $20.35$

2 Answers

Best answer
12 votes
12 votes
  • $3x+2y=14\rightarrow(1)$
  • $2x−3y=5\rightarrow(2)$

To get the intersection point, we solve the equations and get $x=4,y=1$

We can draw the required area like this 

 

From the above diagram,

Area $=\triangle ABC +\Box OBCE-\triangle CDE$

Area $=\left(\dfrac{1}{2}\times 4\times 6\right)+\left(1\times 4\right)-\left(\dfrac{1}{2}\times\dfrac{3}{2}\times 1\right)$

Area $=12+4-\dfrac{3}{4}=16-0.75=15.25$

So, the correct answer is $(B).$

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