Question

QUEM RESPONDER DEIXO A MELHOR RESPOSTA! sendo U= QXQ, resolva os sistemas, aplicando o método de substituição.

a) {x+2y=-3/2}
{3x-y=-7/2}

Answer 1

$\left\{\! \begin{array}{lc} x+2y=-\,\dfrac{3}{2}&~~~~\mathbf{(i)}\\\\ 3x-y=-\,\dfrac{7}{2}&~~~~\mathbf{(ii)} \end{array} \right.$


Isole $y$ na equação $\mathbf{(ii)}$ e substitua na equação $\mathbf{(i)}:$

$y=3x+\dfrac{7}{2}\\\\\\\\ x+2\cdot \left(3x+\dfrac{7}{2} \right )=-\,\dfrac{3}{2}\\\\\\ x+6x+7=-\,\dfrac{3}{2}\\\\\\ 7x+7=-\,\dfrac{3}{2}\\\\\\ 7x=-\,\dfrac{3}{2}-7$


Multiplique os dois lados da equação por 2, para eliminar o denominador

$7x\cdot 2=\left(-\,\dfrac{3}{2}-7 \right )\cdot 2\\\\\\ 14x=-3-14\\\\ 14x=-17\\\\ \boxed{\begin{array}{c}x=-\,\dfrac{17}{14} \end{array}}$


Portanto,

$y=3\cdot \left(-\,\dfrac{17}{14} \right )+\dfrac{7}{2}\\\\\\ y=-\,\dfrac{51}{14}+\dfrac{7}{2}\\\\\\ y=-\,\dfrac{51}{14}+\dfrac{49}{14}\\\\\\ y=\dfrac{-51+49}{14}\\\\\\ y=\dfrac{-2}{14}\\\\\\ \boxed{\begin{array}{c}y=-\,\dfrac{1}{7} \end{array}}$


Conjunto solução: $S=\left\{\left(-\,\dfrac{17}{14}\,,-\,\dfrac{1}{7} \right ) \right\}$


Bons estudos! :-)

Answer 2

$Ola' \\ \\ Sendo~o~sistema:~\begin{cases}x+2y=- \frac{3}{2} ~~----\ \textgreater \ (I) \\ 3x-y=- \frac{7}{2} ~----\ \textgreater \ (II) \end{cases} \\ \\ De~(I)~isolando~''x''~temos: \\ \boxed{x=-2y- \frac{3}{2}} ~----\ \textgreater \ (III) \\ \\ Substituindo~(III)~em~(II)~temos: \\ \\ 3(-2y- \frac{3}{2})-y=- \frac{7}{2} ~~--\ \textgreater \ desenvolvendo \\ -7y=1 \\ \boxed{y=- \frac{1}{7}}~~--\ \textgreater \ valor~de~''y'' \\ \\ ====================================== \\ Substituindo~valor~de~''y''~em~(I)~temos: \\ x+2(- \frac{1}{7})=- \frac{3}{2}$

$x- \frac{2}{7}=- \frac{3}{2} \\ \\\boxed{ x=- \frac{17}{14}} ~~---\ \textgreater \ valor~de~''x'' \\ \\ Por~tanto~a soluc\~ao~do~sistema~e':\boxed{\boxed{x=- \frac{17}{14}~~e~~y=- \frac{1}{7}}} \\ \\ Esto~e'~o~par~ordenado~\bigg(- \frac{17}{14}~,~- \frac{1}{7}\bigg) \\ \\ \\ \\ \mathbb{iiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii} \\~~~~~~~~~~~~~~~~~~~~~~~~Espero~ter~ajudado!!$