Solve the following pair of equations $64 p - 45 q = 289; 45 p - 64 q = 365$

p = 0, q = - 5

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p = 4, q = - 5

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p = 1, q = - 5

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p = 2, q = - 5

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Solution

The correct option is C $p = 1, q = - 5$
Solution:
$64 p - 45 q = 289$ .............(1)
$45 p - 64 q = 365$ .............(2)
Adding equation (1) and (2) we get,
$109 p - 109 q = 654$
i.e., $p - q = 6$ .........(3)
Subtracting equation (1) and (2) we get,
$19 p + 19 q = - 76$
i.e., $p + q = - 4$ .........(4)
Adding equation (3) and (4) we get,
$p = 1$
and substituting $p = 1$ in equation (3) we get,
$q = - 5$

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