Question

Resolva os sistemas abaixo pelo método da adição:
x+y=173
x-y=31

x+y=104
x-y=20

x+y=302
x-y=3​

Answer 1

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$+\underline{\begin{cases}\sf x+\diagup\!\!\!y=173\\\sf x-\diagup\!\!\!y=31\end{cases}}\\\sf2x=204\\\sf x=\dfrac{204}{2}\\\huge\boxed{\boxed{\boxed{\boxed{\sf x=102}}}}\\\sf x+y=173\\\sf 102+y=173\\\sf y=173-102\\\huge\boxed{\boxed{\boxed{\boxed{\sf y=71}}}}\\\huge\boxed{\boxed{\boxed{\boxed{\sf S=\{102,71\}}}}}\blue{\checkmark}$

$+\underline{\begin{cases}\sf x+\diagup\!\!\!y=104\\\sf x-\diagup\!\!\!y=20\end{cases}}\\\sf2x=124\\\sf x=\dfrac{124}{2}\\\huge\boxed{\boxed{\boxed{\boxed{\sf x=62}}}}\blue{\checkmark}\\\sf x+y=104\\\sf 62+y=104\\\sf y=104-62\\\huge\boxed{\boxed{\boxed{\boxed{\sf y=42}}}}\\\huge\boxed{\boxed{\boxed{\boxed{\sf S=\{62,42\}}}}}\blue{\checkmark}$

$+\underline{\begin{cases}\sf x+\diagdown\!\!\!y=302\\\sf x-}\diagdown\!\!\!y=3\end{cases}$

$\sf 2x=305\\\huge\boxed{\boxed{\boxed{\boxed{\sf x=\dfrac{305}{2}}}}}\\\sf x-y=3\\\sf\dfrac{305}{2}-y=3\cdot2\\\sf 305-2y=6\\\sf 2y=305-6\\\sf 2y=299\\\huge\boxed{\boxed{\boxed{\boxed{\sf y=\dfrac{299}{2}}}}}\\\huge\boxed{\boxed{\boxed{\boxed{\sf S=\bigg\{\dfrac{305}{2},\dfrac{299}{2}\bigg\}}}}}\blue{\checkmark}$