One equation of a pair of dependent linear equations is –5x + 7y = 2. The second equation can be ______.

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One equation of a pair of dependent linear equations is –5x + 7y = 2. The second equation can be 10x – 14y = –4. Explanation: Given equation of line is –5x + 7y – 2 = 0 Compare with a1x + b1y + c1 = 0 We get a1 = –5 b1 = 7 c1 = –2 Since condition for dependent linear equation is `a_1/a_2 = b_1/b_2 = c_1/c_2 = 1/k $\therefore$ 5/a_2 = 7/b_2 = -2/c_2 = 1/k` $\Rightarrow$ a2 = –5 b2 = 7k c2 = –2k Where, k is any arbitrary constant. Substituting k = 2, then a2 = –10 b2 = 14 And c2 = –4 $\therefore$ The required equation of line becomes – 10x + 14y – 4 = 0 $\Rightarrow$ 10x – 14y + 4 = 0 $\Rightarrow$ 10x – 14y = –4

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