Solve the following simultaneous equations: 148/x + 231/y = 527/(xy) ; 231/x + 148/y = 610/(xy)

Solve the following simultaneous equations.

\[\frac{148}{x} + \frac{231}{y} = \frac{527}{xy}\]\[\frac{231}{x} + \frac{148}{y} = \frac{610}{xy}\]

Doubtly Asked 24 Oct 2026 Save WhatsApp Report

1 answer

Answer: \((x, y) = (1, 2)\)

Multiply both equations by \(xy\) (\(x, y \neq 0\)):

\(148y + 231x = 527\), i.e. \(231x + 148y = 527\) ... (I)
\(231y + 148x = 610\), i.e. \(148x + 231y = 610\) ... (II)

Adding: \(379x + 379y = 1137\), so \(x + y = 3\) ... (III).
Subtracting (II) from (I): \(83x - 83y = -83\), so \(x - y = -1\) ... (IV).

Adding (III) and (IV): \(2x = 2\), \(x = 1\); then \(y = 2\).

Doubtly AI · 24 Oct 2026 AI-verified · Oct 2026 Report

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