Find the equation of the line passing through the point of intersection of the lines 4x + 7y -3 = 0 and 2x - 3y +1 = 0 that has the equal intercepts on the axes.

Another Explanation (5): ```html

প্রদত্ত সরলরেখাগুলো

\(4x + 7y - 3 = 0\) .................(1)

\(2x - 3y + 1 = 0\) .................(2)

বজ্রগুণন পদ্ধতিতে,

\(\frac{x}{(7 \times 1) - (-3 \times -3)} = \frac{y}{(-3 \times 2) - (4 \times 1)} = \frac{1}{(4 \times -3) - (7 \times 2)}\)

\(\frac{x}{7 - 9} = \frac{y}{-6 - 4} = \frac{1}{-12 - 14}\)

\(\frac{x}{-2} = \frac{y}{-10} = \frac{1}{-26}\)

\(x = \frac{-2}{-26} = \frac{1}{13}\)

\(y = \frac{-10}{-26} = \frac{5}{13}\)

সুতরাং, ছেদবিন্দু \(\left(\frac{1}{13}, \frac{5}{13}\right)\). 🎉

ধরি, সরলরেখার সমীকরণ \(\frac{x}{a} + \frac{y}{a} = 1\)

বা, \(x + y = a\) .................(3)

যেহেতু সরলরেখাটি \(\left(\frac{1}{13}, \frac{5}{13}\right)\) বিন্দুগামী, তাই

\(\frac{1}{13} + \frac{5}{13} = a\)

\(a = \frac{6}{13}\)

(3) নং সমীকরণে \(a\) এর মান বসিয়ে পাই,

\(x + y = \frac{6}{13}\)

\(13x + 13y = 6\). 🥳

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