Solve the following systems of equations.
$4^{x + y} = 128, 5^{3 x - 2 y - 3} = 1$

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Solution

$4^{x + y} = 128, 5^{3 x - 2 y - 3} = 1$
$2^{2 (x + y)} = 2^{7} 5^{3 x - 2 y - 3} = 5^{0}$
$2 (x + y) = 73 x - 2 y - 3 = 0$
$2 x + 2 y = 7$
$3 x - 2 y = 3$
___________
$5 x = 10 \Rightarrow x = 2$
$y = 3 / 2$
$(x, y) = (2, 3 / 2)$

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