Question

Qua a solução deste sistema pelo método da adição 4x+2y=-7 2x+3y=-0,5

Answer 1

$\Large\boxed{\begin{array}{l}\rm Qual~a~soluc_{\!\!,}\tilde ao~deste~sistema\\\rm pelo~m\acute etodo~da~adic_{\!\!,}\tilde ao?\\\begin{cases}\sf4x+2y=-7\\\sf2x+3y=-0,5\end{cases}\end{array}}$

$\boxed{\begin{array}{l}\underline{\boldsymbol{soluc_{\!\!,}\tilde ao\!:}}\\\sf vamos~multiplicar~a~2^a~equac_{\!\!,}\tilde ao~por~-2:\\+\underline{\begin{cases}\sf \diagdown\!\!\!\!\!4\!x+2y=-7\\\sf -\diagdown\!\!\!\!\!\!4\!x-6y=1\end{cases}}\\\sf -4y=-6\cdot(-1)\\\sf 4y=6\\\sf y=\dfrac{6\div2}{4\div2}\\\\\sf y=\dfrac{3}{2}\\\sf Substituindo~na~1^a~equac_{\!\!,}\tilde ao~temos:\\\sf 4x+\backslash\!\!\!2\cdot\dfrac{3}{\backslash\!\!\!2}=-7\\\sf 4x=-7-3\\\sf 4x=-10\\\sf x=-\dfrac{10\div2}{4\div2}\end{array}}$

$\Large\boxed{\begin{array}{l}\sf x=-\dfrac{5}{2}\\\\\sf S=\bigg\{-\dfrac{5}{2},\dfrac{3}{2}\bigg\}\end{array}}$