Question

Tenho muita dificuldade em matematica.

Sistema de equaçoes. 7ª série = 8° ano.

A) \left \{ {{x+y=12} \atop {x-y=2}} \right.

B) \left \{ {{x=2y} \atop {x+y=12}} \right.

C) \left \{ {{x+y=5} \atop {x+3y=11}} \right.

D) \left \{ {{y=3x} \atop {x-y=-6}} \right.

E) \left \{ {{x+y=7} \atop {x+3y=11}} \right.

F) \left \{ {{x+2y=5} \atop {2x+y=-2}} \right.

G) \left \{ {{5x+y=-1} \atop {3x+4y=13}} \right.

H) \left \{ {{2(x-3)+y=-15} \atop {x/4=x+y/6+2/3}} \right.

I) \left \{ {{2x-5y=11} \atop {3x+4y=3}} \right.

Answer 1

Resposta:

$A)~metodo~da~adicao\\ \\~~~~~~~~x+y=12\\+~~~~x-y=~~2\\~~~~~~~~-----\\~~~~~~~2x+0=14\\ \\2x=14\\ \\x=\frac{14}{2}\\ \\x=7\\ \\substitua~(x=7)~em~uma~das~equacoes:\\ \\x+y=12\\ \\7+y=12\\ \\y=12-7\\ \\y=5\\ \\S~\left \{ {{x=7;~~y=5} \} \right.$

$B)~metodo~da~substituicao\\ \\substitua~(x=2y)~em~(x+y=12)\\ \\2y+y=12\\ \\3y=12\\ \\ y=\frac{12}{3}\\ \\y=4\\ \\substitua~(y=4)~em~(x=2y)\\ \\x=2~.~4\\ \\x=8\\ \\S\left \{ {{x=8;~~y=4} \} \right.$

$C)~metodo~da~substituicao\\ \\x+y=5~...~equacao~I\\x+3y=11~...~equacao~II\\ \\na~equacao~I\\ \\x=5-y\\ \\substitua~(x=5-y)~na~equacao~II\\ \\equacao~II\\ \\x+3y=11\\ \\5-y+3y=11\\ \\2y=11-5\\ \\2y=6\\ \\y=\frac{6}{2}\\ \\y=3\\ \\substitua~(y=3)~na~equacao~I\\ \\equacao~I\\ \\x+y=5\\ \\x+3=5\\ \\x=5-3\\ \\x=2\\ \\S~\left \{ {{x=2;~~y=3} \} \right.$

$D)~metodo~da~substituicao\\ \\substitua~(y=3x)~em~(x-y=-6)\\ \\x-3x=-6\\ \\-2x=-6~~.~(-1)\\ \\2x=6\\ \\x=\frac{6}{2}\\ \\x=3\\ \\substitua~(x=3)~em~(y=3x)\\ \\y=3~.~3\\ \\y=9\\ \\S~\left \{ {{x=3;~~y=9} \} \right.$

$E)~metodo~da~substituicao\\ \\x+y=7~...~equacao~I\\x+3y=11~...~equacao~II\\ \\na~equacao~I\\ \\x=7-y\\ \\substitua~(x=7-y)~na~equacao~II\\ \\equacao~II\\ \\x+3y=11\\ \\7-y+3y=11\\ \\2y=11-7\\ \\2y=4\\ \\y=\frac{4}{2}\\ \\y=2\\ \\substitua~(y=2)~na~equacao~I\\ \\equacao~I\\ \\x+y=7\\ \\x+2=7\\ \\x=7-2\\ \\x=5\\ \\S\left \{ {{x=5;~~y=2} \} \right.$

$F)~metodo~da~substitucao\\ \\x+2y=5~...~equacao~I\\2x+y=-2~...~equacao~II\\ \\na~equacao~I\\ \\x=5-2y\\ \\substitua~(x=5-2y)~na~equacao~II\\ \\equacao~II\\ \\2x+y=-2\\ \\2~.~(5-2y)+y=-2\\ \\10-4y+y=-2\\ \\-3y=-2-10\\ \\-3y=-12~~.~(-1)\\ \\3y=12\\ \\y=\frac{12}{3}\\ \\y=4\\ \\substitua~(y=4)~na~equacao~I\\ \\equacao~I\\ \\x+2y=5\\ \\x+2~.~4=5\\  \\x+8=5\\ \\x=5-8\\ \\x=-3\\ \\S~\left \{ {{x=-3;~~y=4} \} \right.$

$G)~metodo~da~substituicao\\ \\na~equacao~I\\ \\5x+y=-1\\ \\y=-1-5x\\ \\substitua~(y=-1-5x)~em~(3x+4y=13)\\ \\3x+4.(-1-5x)=13\\ \\3x-4-20x=13\\ \\-17x=13+4\\ \\-17x=17\\ \\x=-\frac{17}{17}\\ \\x=-1\\ \\substitua~(x=-1)~em~(5x+y=-1)\\ \\5.(-1)+y=-1\\ \\-5+y=-1\\ \\y=-1+5\\ \\y=4\\ \\S\left \{ {{x=-1;~~y=4} \} \right.$

$H)~~*(nao~entendi~o~enunciado)$

$I)~metodo~da~comparacao\\ \\na~equacao~I\\ \\2x-5y=11\\ \\2x=11+5y\\ \\x=\frac{11+5y}{2}\\ \\ \\na~equacao~II\\ \\3x+4y=3\\ \\3x=3-4y\\ \\x=\frac{3-4y}{3}\\ \\ \\x=x~~~~logo:\\\\\frac{11+5y}{2}=\frac{3-4y}{3}\\ \\ 3~.~(11+5y)=2~.~(3-4y)\\ \\33+15y=6-8y\\ \\15y+8y=6-33\\ \\23y=-27\\ \\y=-\frac{27}{23}\\ \\substitua~(y=-\frac{27}{23})~em~uma~das~equacoes:\\  \\equacao~I\\ \\2x-5y=11\\ \\2x-2(-\frac{27}{23})=11\\ \\2x+\frac{54}{23}=11$

$mmc=23\\ \\\frac{46x+54=253}{23}\\ \\despreze~o~denominador\\ \\ 46x+54=253\\ \\46x=253-54\\ \\46x=199\\ \\x=\frac{199}{46}\\ \\S\left \{ {{x=\frac{199}{46};~~y=-\frac{27}{23}} \} \right.$