Question

Resolva os sistemas pelo métido da substituição.
A)x+y=11
x-y=3
B)x+y=6
2×+y=4
C)3×+y=5
2×+y=4
D)x-y=6
x+y=-7
E)x=5-3y
2x-y=-7
F)×-3=-y
3×+2=y+3​

Answer 1

Resposta:

OBS: Não consegui fazer todas... Se quiser saber como fazer vai nesse link https://www.youtube.com/watch?v=BGCmEYN_Uho

A) S= { ( 7, 4 ) }

B) S= { ( -4, 10 ) }

D) S= { ( -0.5, 6.5 )}

F) S= { ( 5.5, 8.5 ) }

Explicação passo-a-passo:

Answer 2

Resposta:

$A)\\ \\ x+y=11.....eq~I\\ x-y=3......eq~II\\ \\ eq~I\\ \\ x=11-y\\ \\ eq~II\\ \\ (11-y)-y=3\\ \\ -y-y=3-11\\ \\ -2y=-8~(-1)\\ \\ 2y=8\\ \\ y=\frac{8}{2} \\ \\ y=4\\ \\ eq~I\\ \\ x+y=11\\ \\ x+4=11\\ \\ x=11-4\\ \\ x=7\\ \\ S~~(x=7;~~y=4)$

$B)\\ \\ x+y=6....eq~I\\ 2x+y=4....eq~II\\ \\ eq~I\\ \\ x=6-y\\ \\ eq~II\\ \\ 2(6-y)+y=4\\ \\ 12-2y+y=4\\ \\ -2y+y=4-12\\ \\ -y=-8~.(-1)\\ \\ y=8\\ \\ eq~I\\ \\ x+y=6\\ \\ x+8=6\\ \\ x=6-8\\ \\ x=-2\\ \\ S~~(x=-2;~~y=8)$

$C)\\ \\ 3x+y=5...eq~I\\ \\ 2x+y=4...eq~II\\ \\ eq~I\\ \\ y=5-3x\\ \\ eq~II\\\\  2x+5-3x=4\\ \\ 2x-3x=4-5\\ \\ -x=-1~.(-1)\\ \\ x=1\\ \\ eq~I\\ \\ 3x+y=5\\ \\ 3.1+y=5\\ \\ y=5-3\\ \\ y=2\\ \\ S~(x=1;~~y=2)$

$D)\\ \\ x-y=6.....eq~I\\ x+y=-7....eq~II\\ \\ eq~I\\ \\ x=6+y\\ \\ eq~II\\ \\ 6+y+y=-7\\ \\ 2y=-7-6\\ \\ 2y=-13\\ \\ y=-\frac{13}{2} \\ \\ eq~I\\ \\ x-y=6\\ \\ x-(-\frac{13}{2})=6\\ \\ x+\frac{13}{2}=6\\ \\ x=6-\frac{13}{2} \\ \\ mmc=2\\ \\ x=\frac{12-13}{2} \\ \\ x=-\frac{1}{2} \\ \\ S~(x=-\frac{1}{2};~~y=-\frac{13}{2})$

$E)\\ \\ x=5-3y.....eq~I\\ 2x-y=-7.....eq~II\\ \\ na~eq~II\\ \\ 2(5-3y)-y=-7\\ \\ 10-6y-y=-7\\ \\ -6y-y=-7-10\\ \\ -7y=-17(-1)\\ \\ 7y=17\\ \\ y=\frac{17}{7} \\ \\ na~eq~I\\ \\ x=5-3y\\ \\ x=5-3.(\frac{17}{7})\\  \\ x=5-\frac{51}{7} \\ \\ mmc=7\\ \\ x=\frac{35-51}{7} \\ \\ x=-\frac{16}{7} \\ \\ S~(x=-\frac{16}{7};~~y=\frac{17}{7})$

$F)\\ \\ x-3=-y...eq~I\\ 3x+2=y+3...eq~II\\ \\ na~eq~II\\ \\ 3x-y=3-2\\ \\ 3x-y=1....eq~II\\ \\ na~eq~I\\ \\ x=-y+3\\ \\ na~eq~II\\ \\ 3.(-y+3)-y=1\\ \\ -3y+9-y=1\\ \\ -3y-y=1-9\\ \\ -4y=-8~.(-1)\\ \\ 4y=8\\ \\ y=\frac{8}{4} \\ \\ y=2\\ \\ na~eq~I\\ \\ x-3=-y\\ \\ x-3=-2\\ \\ x=-2+3\\ \\ x=1\\ \\ S~(x=1;~~y=2)$