Question

Resolva este sistema de equação pelo método da adição.
$\left \{ {{3a + b = 2} \atop {-a +b = 0}} \right.$

Answer 1

$\left \{ {{3a+b=2}\,\,\,(I)\atop {-a+b=0}\,\,\,\,\,\,(II)} \right.$

Multiplicando II por (-1)

$-a+b=0\,\,\,.\,\,(-1)\\\\a-b=0$

Podemos somar a nova equação com I e teremos

$3a+a+b-b=2\\\\4a=2\\\\a= \dfrac{2}{4}\\\\\\ a= \dfrac{1}{2}$

$-a+b=0\\\\- \dfrac{1}{2}+b=0\\\\\\-1+2b=0\\\\2b=1\\\\b= \dfrac{1}{2}\\\\\boxed{S=\bigg\{\bigg( \dfrac{1}{2},\dfrac{1}{2}\bigg)\bigg\}}$