Question

Resolva estes sistemas
a) x= 5y
x+y=12
b) x-y= 10
2x+3y= 10
c) x= y+3
4x+y= -3
d) x+y= 3
12x-9y= -20
e) 2x+y= 3
5x - 2y = -5
f) x - y = 4
2x - 4y = 13
g) x + y= 6
2x - y = 24
h) x + 2y = 5
x + 3y = 8
i) 3x + 4y= -5
x - 2y = 5
j) x + 3y= 6
-4x + 6y= -12

Answer 1

$a)\\\\x=5y\\\\x+y=12\\\\substitua~(x=5y)~em~(x+y=12)\\\\5y+y=12\\\\6y=12\\\\y=\frac{12}{6}\\\\y=2\\\\substitua~(y=2)~em~(x=5y)\\\\x=5~.~2\\\\x=10~~~~~~~~~~S=(y=2;~~x=10)$

$b)\\\\x-y=10~......~equacao~I\\\\2x+3y=10~....~equacao~II\\\\Na~equacao~I:\\\\x=y+10\\\\Substitua~(x=y+10)~na\\\\equacao~II\\\\2x+3y=10\\\\2.(y+10)+3y=10\\\\2y+20+3y=10\\\\2y+3y=10-20\\\\5y=-10\\\\y=-\frac{10}{5}\\\\y=-2\\\\substitua~(y=-2)~na~equacao~I\\\\x-y=10\\\\x-(-2)=10\\\\x+2=10\\\\x=10-2\\\\x=8~~~~~~~~~~S=(x=8;~~y=-2)$

$c)\\\\x=y+3\\\\x+y=-3\\\\substitua~(x=y+3)~em~(x+y=-3)\\\\y+3+y=-3\\\\2y=-\frac{3}{3}\\\\2y=0\\\\y=0\\\\substitua~(y=0)~em~(x=y+3)\\\\x=0+3\\\\x=3~~~~~~~~~~~~~~S=(x=3;~~y=0)$

$d)\\\\x+y=3\\\\12x-9y=-20\\\\x=3-y\\\\substitua~(x=3-y)~em~(12x-9y=-20)\\\\12.(3-y)-9y=-20\\\\36-12y-9y=-20\\\\-12y-9y=-20-36\\\\-21y=-56~.~(-1)\\\\21y=56~~~~~~~~~~~~~~simplifique~por~7\\\\3y=8\\\\y=\frac{8}{3}\\\\substitua~(y=\frac{8}{3})~em~(x+y=3)\\\\x+\frac{8}{3}=3\\\\x=3-\frac{8}{3}\\\\mmc=3\\\\x=\frac{9-8}{3}\\\\x=\frac{1}{3}~~~~~~~~~S=(x=\frac{1}{3};~~y=\frac{8}{3})$

$e)\\\\2x+y=3\\\\5x-2y=-5\\\\Metodo~da~adicao:\\\\multiplique~a~equacao~I~por~2~e~some~as~equacoes\\\\~~~~~~~~~~4x+2y=~~6\\~+~~~~~5x-2y=-5\\~~~~~~~-------\\~~~~~~~~~~9x+~0=~~1\\\\9x=1\\\\x=\frac{1}{9}\\\\substitua~(x=\frac{1}{9})~em~uma~das~equacoes:\\\\2x+y=3\\\\2.\frac{1}{9}+y=3\\\\y=3-\frac{2}{9}\\\\mmc=9$

$y=\frac{27-2}{9}=\frac{25}{9}~~~~~~~~S=(x=\frac{1}{9};~~y=\frac{25}{9})$

$Muitas~questoes.\\\\Depois~continuo...$