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Given the equations 2^y−x = 16 and 4^y+x = 8. We need to find the value of x+y.

March 30, 2026Mathematics

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:
Given the equations $2^{y-x} = 16$ and $4^{y+x} = 8$ . We need to find the value of $x+y$ .

Rewrite the first equation with a common base.
$2^{y-x} = 16$
Since $16 = 2^4$ , we have:
$2^{y-x} = 2^4$
Equating the exponents:
$y-x = 4 \quad (*)$
Rewrite the second equation with a common base.
$4^{y+x} = 8$
Since $4 = 2^2$ and

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