GATE 2016 EC (EC3) – Question 9

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

Show answer and explanation

Correct answer: (B) 15.25

Explanation

The lines intersect at (4,1). In the first quadrant, the enclosed region uses the axes and has vertices (0,0), (5/2,0), (4,1) and (0,7).

The shoelace area is $\tfrac12[(5/2)(1)+4(7)]=30.5/2=$ **15.25 square units, B**. The first-quadrant axes close the region implied by the question.

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