With a = 1/x and b = 1/y, the pair 2/x + 3/y = 13 and 5/x - 4/y = -2 becomes 2a + 3b = 13 and 5a - 4b = -2. Solve it by elimination. Find a (= 1/x).

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Accepted Answer

2. Multiply first by 4 (8a+12b=52), second by 3 (15a-12b=-6); add: 23a = 46, so a = 2.

With $a = \frac{1}{x}$ and $b = \frac{1}{y}$ , the pair $\frac{2}{x} + \frac{3}{y} = 13$ and $\frac{5}{x} - \frac{4}{y} = - 2$ becomes $2 a + 3 b = 13$ and $5 a - 4 b = - 2$ . Solve it by elimination.
Find a (= $\frac{1}{x}$ ).