Discussion

Explanation:

The intersection of the lines x + 2y = 4 and 2x + 3y = 6 is (0, 2)

Slope of line 3x – y = 2 is 3. Slope of line perpendicular to this line is -1/3 [Product of slopes of two perpendicular lines = -1]

Now, we need to find the x-intercept of a line passing through (0, 2) whose slope is -1/3

Let the x-intercept be (a, 0)

⇒​ Slope of the line passing through (a, 0) and (0, 2) = - 1/3

⇒​ $\frac{0-2}{\mathrm{a}-0}$ = $-\frac{1}{3}$

⇒​ a = 6

Hence, option (d).

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