Question

Urgente pra hoje
Resolva os sistemas a seguir:
A) 5x=4-2y
3y=2x+3

B) 5x + 2y = 3+4y
4x - 3y + 1 = x-y

C) x+y=x-1
2
y-1=2x-y+1
2

Answer 1

$A)\\ \\ 5x+2y=4~...~equacao~I\\ \\ 2x-3y=-3~.....~equacao~II\\ \\ podemos~usar~o~metodo~da~comparacao\\ \\ equacao~I\\ \\ 5x+2y=4\\ \\ 5x=4-2y\\ \\ x=\frac{4-2y}{5} \\ \\ equacao~II\\ \\ 2x-3y=-3\\ \\ 2x=-3+3y\\ \\ x=\frac{-3+3y}{2} \\ \\ x=x\\ \\ \frac{4-2y}{5} =\frac{-3+3y}{2} \\ \\ 2(4-2y)=5(-3+3y)\\ \\ 8-4y=-15+15y\\ \\ -4y-15y=-15-8\\ \\ -19y=-23(-1)\\ \\ 19y=23\\ \\ y=\frac{23}{19}$

$substitua~(y=\frac{23}{19} )~em~uma~das~equacoes:\\ \\ 5x=4-2y\\ \\ 5x=4-2(\frac{23}{19} )\\ \\ 5x=4-\frac{46}{19} \\ \\ mmc=19\\ \\ \frac{95x=76-46}{19} \\ \\ 95x=30\\ \\ x=\frac{30}{95} =\frac{6}{19} \\ \\ S=(x=\frac{6}{19} ,~~y=\frac{23}{19} )$

$B)\\ \\ 5x+2y=3+4y\\ \\ 5x+2y-4y=3\\ \\ 5x-2y=3~......~equacao~I\\ \\ 4x-3y+1=x-y\\ \\ 4x-3y-x+y=-1\\ \\ 3x-2y=-1~......~equacao~II\\ \\ metodo~da~adicao~(multiplique~a~equacao~I~por~(-1)\\ \\ 5x-2y=3~.(-1)\\ \\ ~~~~~~~-5x+2y=-3\\ ~+~~~~~~3x-2y=-1\\ ~~~~~~~~--------\\ ~~~~~~~~-2x+0=-4\\ \\ -2x=-4~.(-1)\\ \\ 2x=4\\ \\ x=\frac{4}{2}\\\\ x=2 \\ \\ substitua~x=2~em~uma~das~equacoes\\ \\ 3x-2y=-1\\ \\ 3.2-2y=-1\\ \\ 6-2y=-1\\ \\ -2y=-1-6\\ \\ -2y=-7\\ \\ 2y=7\\ \\ y=\frac{7}{2}$

$S=(x=2,~~y=\frac{7}{2} )$

$C)\\\\\frac{x+y}{2} =x-1 \\ \\ y-1=\frac{2x-y+1}{2} \\ \\ x+y=2(x-1)\\ \\ x+y=2x-2\\ \\ x-2x+y=2\\ \\ -x+y=2~.....~equacao~I\\ \\ y-1=\frac{2x-y+1}{2} \\ \\ 2(y-1)=2x-y+1\\ \\ 2y-2=2x-y+1\\ \\ 2y-y-2x=1+2\\ \\ y-2x=3~.....~equacao~II\\ \\ metodo~da~substituicao\\ \\ na~equacao~I\\ \\ -x+y=2(-1)\\ \\ x-y=-2\\ \\ x=-2+y\\ \\ substitua~(x=-2+y)~na~equacao~II\\ \\ y-2x=3\\ \\ y-2(-2+y)=3\\ \\ y+4-2y=3\\ \\ -y=-1\\ \\ y=1$

$na~equacao~I\\ \\ -x+y=2\\ \\ -x+1=2\\ \\ -x=2-1\\ \\ -x=1~.(-1)\\ \\ x=-1\\ \\ S=(x=-1,~~y=1)$