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The ratio of the areas of the two triangles formed by the lines representing the equations $2 x + y = 6$ and $2 x − y + 2 = 0$ with the X -axis and the lines with the $Y$ -axis is

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2 : 1

3 : 5

4 : 1

5 : 2

answer is C.

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Detailed Solution

Given pair of equations are

2 x + y − 6 = 0 … (i) 2 x − y + 2 = 0 … (i i)

The graphical representation of given equations is,
Question Image

The point of intersection of both the lines and with x-axis or y-axis gives vertices of the triangle.

Then, area of Δ A C E = 12 × A C × P E = 12 × 4 × 4 = 8 s q And area of Δ B D E = 12 × B D × Q E = 12 × 4 × 1 = 2 s q units

Ratio of Area of triangles is = 82 Ratio of Area of triangles is = 4 : 1

Therefore, the ratio of area of triangles is

4 : 1

.
Hence, option (3) is correct.

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