Question

ache o valor de x e y 

(a). 2x-y= 3                          (b). 2x=3y               (c).y=3x+2
     3x+2y= 8                             x+y= 50                  2x-y= -4

Answer 1

Olá Natália,

no 1º sistema multiplique a equação I por 2 e some as duas equações:

$\begin{cases}4x-2y=6~~(I)\\ 3x+2y=8~~(II)\end{cases}\\ ~~------\\ ~~~~7x~~~~~~=14\\\\ ~~~~~~~x= \dfrac{14}{7}\\\\ ~~~~~~~~x=2\\\\ 3x+2y=8\\ 3\cdot2+2y=8\\ 6+2y=8\\ 2y=8-6\\ 2y=2\\\\ y= \dfrac{2}{2}\\\\ y=1\\\\\\ \large\boxed{\boxed{S=\{(2,1)\}}}\\.$

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no 2º, isole x na equação II, e substitua na equação I:

$\begin{cases}2x=3y~~(I)\\x=50-y~~(II)\end{cases}\\\\ 2(50-y)=3y\\ 100-2y=3y\\ 3y+2y=100\\ 5y=100\\\\ y= \dfrac{100}{5}\\\\ y=20\\\\ x=50-y\\ x=50-20\\ x=30\\\\\\ \large\boxed{\boxed{S=\{(30,20)\}}}\\.$

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Se y vale 3x+2 na equação I, podemos substituí-lo na equação II:

$2x-(3x+2)=-4\\ 2x-3x-2=-4\\ 2x-3x=-4+2\\ -x=-2~~\cdot~~(-1)\\\\ x=2\\\\ y=3x+2\\ y=3\cdot2+2\\ y=6+2\\ y=8\\\\\\ \large\boxed{\boxed{S=\large\{(2,8)\}}}\\.$

Tenha ótimos estudos =))