Question

Resolva o sistema usando o processo de escalamento

2x + 2y+ 3z= 5
X + y + 2z= 3
3x + 4y +2z= 0

Answer 1

$\large\boxed{\begin{array}{l}\begin{cases}\sf 2x+2y+3z=5\\\sf x+y+2z=3\\\sf 3x+4y+2z=0\end{cases}\\\\\begin{cases}\sf x+y+2z=3\\\sf2x+2y+3z=5\\\sf 3x+4y+2z=0\end{cases}\\\\\begin{cases}\sf x+y+2z=3\\\sf-z=-1\implies z=1\\\sf-2y-4z=-9\implies 2y+4z=9\end{cases}\end{array}}$

$\large\boxed{\begin{array}{l}\sf2y+4z=9\\\sf 2y+4\cdot1=9\\\sf 2y+4=9\\\sf 2y=9-4\\\sf 2y=5\\\sf y=\dfrac{5}{2}\\\\\sf x+y+2z=3\\\sf x+\dfrac{5}{2}+2\cdot1=3\cdot(2)\\\\\sf 2x+5+2=6\\\sf 2x+7=6\\\sf 2x=6-7\\\sf 2x=-1\\\sf x=-\dfrac{1}{2}\\\\\sf S=\bigg\{-\dfrac{1}{2},\dfrac{5}{2},1\bigg\}\end{array}}$