If 2x+3y=13, 5x−4y=−2, then x=

2x+3y=13, 5x−4y=−2Let 1x=a ; 1y=b2a+3b=13→(1)5a−4b=−2→(2)Solve (1)&(2)2a+3b=13→(1)×45a−4b=−2→(2)×38a +12b =5215a−12b=−6_23a =46a=2, b=93=3∴a=1x=2⇒x=12b=1y=3⇒y=13

If 2x+3y=13, 5x−4y=−2, then x=

2x+3y=13, 5x−4y=−2Let 1x=a ; 1y=b2a+3b=13→(1)5a−4b=−2→(2)Solve (1)&(2)2a+3b=13→(1)×45a−4b=−2→(2)×38a +12b =5215a−12b=−6_23a =46a=2, b=93=3∴a=1x=2⇒x=12b=1y=3⇒y=13

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If $\frac{2}{x} + \frac{3}{y} = 13, \frac{5}{x} - \frac{4}{y} = - 2$ , then $x =$

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$\frac{1}{5}$

$\frac{1}{2}$

$\frac{1}{3}$

$\frac{1}{4}$

answer is A.

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Detailed Solution

$\begin{array}{l} \frac{2}{x} + \frac{3}{y} = 13, \frac{5}{x} - \frac{4}{y} = - 2 \\ L e t \frac{1}{x} = a; \frac{1}{y} = b \\ 2 a + 3 b = 13 \to (1) \\ 5 a - 4 b = - 2 \to (2) \\ S o l v e (1) & (2) \\ 2 a + 3 b = 13 \to (1) \times 4 \\ 5 a - 4 b = - 2 \to (2) \times 3 \\ \underline{\begin{array}{l} 8 a + 12 b = 52 \\ 15 a - 12 b = - 6 \end{array}} \\ 23 a = 46 \\ a = 2, b = \frac{9}{3} = 3 \\ ∴ a = \frac{1}{x} = 2 \Rightarrow x = \frac{1}{2} \\ b = \frac{1}{y} = 3 \Rightarrow y = \frac{1}{3} \end{array}$