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Solve: \( \frac{a x}{b}-\frac{b y}{a}=a+b, a x-b y=2 a b \). |
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Answer» \(\frac{ax}{b} - \frac{by}{a} = a + b\) ....(1) \(ax - by = 2ab\) ....(2) From (2), we get \(\frac{ax - by}{a} = 2b\) ⇒ \(x - \frac ba y = 2b\) .....(3) Subtract equation (3) from (1), we obtain \(\left(\frac ab -1\right)x = a - b\) ⇒ \(\left(\frac {a-b}b\right)x = a - b\) ⇒ x = b ∴ From (3), we get \(b - \frac ba y = 2b\) ⇒ \( \frac ba y = b-2b\) ⇒ \( \frac ba y = -b\) ⇒ y = -a Hence, x = b, y = -a be solution of given system of equations. |
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