Question

Considere o método da substituição e resolva os sistemas abaixo
a)
{x+y=24

{x-3y= -16
b)
{x=3y

{2x+5y=6

Answer 1

$a)\\\\x+y=24~.............~equacao~I \\ x-3y=-16~..........~equacao~II\\\\ na~equacao~I\\\\x=24-y\\\\substitua~(x=24-y)~na~equacao~II\\\\24-y-3y=-16\\\\-4y=-16-24~.~(-1)\\\\4y=16+24\\\\4y=40\\\\y=\frac{40}{4}\\\\y=10\\\\substitua~(y=10)~em~uma~das~equacoes:\\\\equacao~I\\\\x+y=24\\\\x+10=24\\\\x=24-10\\\\x=14\\\\S~=~(x=14;~~y=10)$

$b)\\\\x=3y~...............~equacao~I\\2x+5y=6~.......~equacao~II\\\\substitua~(x=3y)~na~equacao~II\\\\2(3y)+5y=6\\\\6y+5y=6\\\\11y=6\\\\y=\frac{6}{11}\\\\substitua~(y=\frac{6}{11} )~em~uma~das~equacoes:\\\\equacao~I\\\\x=3y\\\\x=3(\frac{6}{11} )\\\\x=\frac{18}{11}\\\\S~=~(y=\frac{6}{11};~~x=\frac{18}{11})$