Find the values of $(m + n)$ and $(m - n)$ without actually solving for $m$ and $n$ .
$17 m + 13 n = 133; 13 m + 17 n = 137$

m + n = 5, m - n = - 1

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m + n = 1, m - n = - 1

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m + n = 2, m - n = - 1

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m + n = 9, m - n = - 1

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Solution

The correct option is D $m + n = 9, m - n = - 1$
$17 m + 13 n = 133$ ...(i)
$13 m + 17 n = 137$ ...(ii)
On adding (i) and (ii) , we get
$30 m + 30 n = 270$
$\Rightarrow m + n = 9$
On subtracting (ii) from (i) , we get
$4 m - 4 n = - 4$
$\Rightarrow m - n = - 1$

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