Question

por favor me ajudem.. serio agradeço de coração a quem responder
{x-y=5
{x²+y=13​

Answer 1

$\boxed{\begin{array}{l}\begin{cases}\sf x-y=5\\\sf x^2+y=13\end{cases}\\\underline{\rm isolando~y~na~1^a~equac_{\!\!,}\tilde ao~temos:}\\\begin{cases}\sf y=x-5\\\sf x^2+y=13\end{cases}\\\underline{\rm substituindo~y~na~2^a~equac_{\!\!,}\tilde ao~temos\!:}\\\sf x^2+x-5=13\\\sf x^2+x-5-13=0\\\sf x^2+x-18=0\\\sf \Delta=b^2-4ac\\\sf\Delta=1^2-4\cdot1\cdot(-18)\\\sf\Delta=1+72\\\sf\Delta=73\\\sf x=\dfrac{-b\pm\sqrt{\Delta}}{2a}\\\sf x=\dfrac{-1\pm\sqrt{73}}{2\cdot1}\end{array}}$

$\boxed{\begin{array}{l}\sf x=\dfrac{-1\pm\sqrt{73}}{2}\begin{cases}\sf x_1=\dfrac{-1+\sqrt{73}}{2}\\\sf x_2=\dfrac{-1-\sqrt{73}}{2}\end{cases}\\\underline{\rm substituindo~x~na~equac_{\!\!,}\tilde ao~y=x-5~temos:}\\\sf se~x_1=\dfrac{-1+\sqrt{73}}{2}:\\\sf y=\dfrac{-1+\sqrt{73}}{2}-5\\\sf y=\dfrac{-1+\sqrt{73}-10}{2}\\\sf y=\dfrac{-11+\sqrt{73}}{2}\\\sf se~x_2=\dfrac{-1-\sqrt{73}}{2}:\\\sf y=\dfrac{-1-\sqrt{73}}{2}-5\\\sf y=\dfrac{-1-\sqrt{73}-10}{2}\\\sf y=\dfrac{-11-\sqrt{73}}{2}\end{array}}$

$\boxed{\begin{array}{l}\sf S=\bigg\{\bigg(\dfrac{-1+\sqrt{73}}{2},\dfrac{-11+\sqrt{73}}{2}\bigg),\bigg(\dfrac{-1-\sqrt{73}}{2},\dfrac{-11-\sqrt{73}}{2}\bigg)\bigg\}\end{array}}$