Question

Resolva pelo método de adição os sistemas, sendo U = Q x Q:​

Answer 1

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$\large\boxed{\begin{array}{l}\rm a)\\+\underline{\begin{cases}\sf x+\diagup\!\!\!y=6\\\sf x-\diagup\!\!\!y=4\end{cases}}\\\sf 2x=10\\\sf x=\dfrac{10}{2}\\\sf x=5\\\sf x+y=6\\\sf 5+y=6\\\sf y=6-5\\\sf y=1\\\sf S=\{5,1\}\end{array}}$

$\large\boxed{\begin{array}{l}\rm b)\\+\underline{\begin{cases}\sf x+\bf\diagdown\!\!\!\!\!2y=\sf5\\\sf3x-\bf\diagdown\!\!\!\!\!2y=\sf-17\end{cases}}\\\sf 4x=-12\\\sf x=-\dfrac{12}{4}\\\sf x=-3\\\sf x+2y=5\\\sf -3+2y=5\\\sf 2y=5+3\\\sf 2y=8\\\sf y=\dfrac{8}{2}\\\sf y=4\\\sf S=\{-3,4\}\end{array}}$

$\large\boxed{\begin{array}{l}\rm c)\\\begin{cases}\sf3x+4y=-5\\\sf x-2y=5\cdot2\end{cases}\\+\underline{\begin{cases}\sf3x+\diagdown\!\!\!\!\!4y=-5\\\sf 2x-\diagdown\!\!\!\!\!4y=10\end{cases}}\\\sf5x=5\\\sf x=\dfrac{5}{5}\\\sf x=1\\\sf x-2y=5\\\sf 1-2y=5\\\sf 2y=1-5\\\sf 2y=-4\\\sf y=-\dfrac{4}{2}\\\sf y=-2\\\sf S=\{1,-2\}\end{array}}$

$\large\boxed{\begin{array}{l}\rm d)\\\begin{cases}\sf x+3y=6\cdot4\\\sf-4x+6y=-12\end{cases}\\+\underline{\begin{cases}\sf\diagdown\!\!\!\!\!\!4x+12y=24\\\sf-\diagdown\!\!\!\!\!\!4x+6y=-12\end{cases}}\\\sf 18y=12\\\sf y=\dfrac{12\div6}{18\div6}\\\sf y=\dfrac{2}{3}\\\sf x+3y=6\\\sf x+\diagup\!\!\!3\cdot\dfrac{2}{\diagup\!\!\!3}=6\\\sf x+2=6\\\sf x=6-2\\\sf x=4\\\sf S=\bigg\{4,\dfrac{2}{3}\bigg\}\end{array}}$

$\boxed{\begin{array}{l}\rm e)\\\begin{cases}\sf3x+4y=19\cdot2\\\sf2x-3y=7\cdot(-3)\end{cases}\\+\underline{\begin{cases}\sf\diagdown\!\!\!\!\!\!6x+8y=38\\\sf-\diagdown\!\!\!\!\!\!6x+9y=-21\end{cases}}\\\sf 17y=17\\\sf y=\dfrac{17}{17}\\\sf y=1\\\sf 2x-3y=7\\\sf 2x-3\cdot1=7\\\sf 2x=7+3\\\sf 2x=10\\\sf x=\dfrac{10}{2}\\\sf x=5\\\sf S=\{5,1\}\end{array}}$

$\large\boxed{\begin{array}{l}\rm f)\\\begin{cases}\sf 2x+3y=26\cdot3\\\sf3x+2y=24\cdot(-2)\end{cases}\\+\underline{\begin{cases}\sf\diagdown\!\!\!\!\!\!6x+9y=78\\\sf-\diagdown\!\!\!\!\!\!6x-4y=-48\end{cases}}\\\sf 5y=30\\\sf y=\dfrac{30}{5}\\\sf y=6\\\sf 2x+3y=26\\\sf 2x+3\cdot6=26\\\sf 2x+18=26\\\sf 2x=26-18\\\sf 2x=8\\\sf x=\dfrac{8}{2}\\\sf x=4\\\sf S=\{4,6\}\end{array}}$