Question

5^3x+2y =1/5
3^x-y=9
quanto é x+y?

Answer 1

$\boxed{\begin{array}{l}\begin{cases}\sf5^{3x+2y}=\dfrac{1}{5}\\\sf 3^{x-y}=9\end{cases}\\\begin{cases}\sf5^{3x+2y}=5^{-1}\\\sf3^{x-y}=3^2\end{cases}\\\begin{cases}\sf 3x+2y=-1\\\sf x-y=2\end{cases}\end{array}}$

$\boxed{\begin{array}{l}+\underline{\begin{cases}\sf 3x+\diagdown\!\!\!\!\!2y=-1\\\sf 2x-\diagdown\!\!\!\!\!2y=4\end{cases}}\\\sf5x=3\\\sf x=\dfrac{3}{5}\\\sf x-y=2\\\sf\dfrac{3}{5}-y=2\cdot5\\\sf3-5y=10\\\sf 5y=3-10\\\sf 5y=-7\\\sf y=-\dfrac{7}{5}\\\sf x+y=\dfrac{3}{5}-\dfrac{7}{5}\\\sf x+y=-\dfrac{4}{5}\blue{\checkmark}\end{array}}$