Question

resolva os sistemas de equação :

Answer 1

Resposta:

respostas na explicação abaixo

Explicação passo-a-passo:

$a) \left \{ {{x + y =3} \atop {x -y=-1}} \right => \left \{ {{x =3} \atop {x =-1}} \right=> 2x=3-1=> 2x = 2 => x = \frac{2}{2} => x = 1\\x + y = 3 => 1 + y = 3 => y = 3 -1 => y = 2$

S = (1, 2)

$b) \left \{ {{x + y =4} \atop {x -y=-2}} \right => \left \{ {{x = 4} \atop {x = -2}} \right=> 2x=4-2=> 2x = 2 => x = \frac{2}{2} => x = 1\\x + y = 4 => 1 + y = 4 => y = 4 -1 => y = 3$

S = (1, 3)

$c) \left \{ {{x - y = -3} \atop {x + y= 5}} \right => \left \{ {{x = -3} \atop {x = 5}} \right=> 2x= -3 + 5=> 2x = 2 => x = \frac{2}{2} => x = 1\\x - y = -3 => 1 + y = -3 => -y = -3 -1 => (-1)(-y) = (-1)(-4) => y = 4$

S = (1, 4)

$d) \left \{ {{-x + y = 4} \atop {x - y= 6}} \right => \left \{ {{y = 4} \atop {y = 6}} \right=> 2y= 4 + 6=> 2y = 10 => y = \frac{10}{2} => y = 5\\x + y = 6 => x + 5 = 6 => x = 6 -5 => => x = 1$

S = (1, 5)

$e) \left \{ {{x - y = -5} \atop {2x - y= 8}} \right =>\left \{ {{x - y = -5(-1)} \atop {2x - y= 8}} \right =>\left \{ {{- x + y = 5} \atop {2x - y= 8}} \right => \left \{ {{- x = 5} \atop {x = 8}} \right=> x = 5 + 8=> x = 13 => x - y = -5 => 13 - y = -5 => y = -5 -13 => => x = -18$

S = (13, 18)

$f) \left \{ {{- x + y =-1} \atop {x + 2y= 4}} \right => \left \{ {{y = -1} \atop {2y = 4}} \right=> 3y = -1 + 4=> 3y = 3 => y = \frac{3}{3} => y = 1\\x + 2y = 4 => x + 2.1 = 4 =>x + 1 = 4 => x = 4 - 1 => x = 3$

S = (1, 2)