Question

resolva utilizando o método da adição
1) {3x+y =5
2x+y =7

2) {2x+y=5
x-3y=6
​

Answer 1

Resposta:

1) x=(-2) e y=11

2) x=3 e y=(-1)

Explicação passo a passo:

$1)\ \left \{ {{3x+y=5} \atop {2x+y=7}} \right. \\\\\\\left \{ {{3x+y(-1)=5(-1)} \atop {2x+y=7}} \right. \\\\\\\left \{ {{-3x-y=(-5)} \atop {2x+y=7}} \right. \\\\\\2x+y+(-3x-y)=7+(-5)\\\\2x+y-3x-y=7-5\\\\2x-3x=2\\\\-x=2\\\\-(-x)=[-(2)]\\\\\bold{x=(-2)}$

$\left \{ {{3x+y=5} \atop {2x+y=7}} \right. \\\\\\\left \{ {{(-2)(3x+y)=(-2)(5)} \atop {3(2x+y)=3(7)}} \right. \\\\\\\left \{ {{-6x-2y=(-10)} \atop {6x+3y=21}} \right. \\\\6x+3y+(-6x-2y)=21+(-10)\\\\6x+3y-6x-2y=21-10\\\\3y-2y=11\\\\\bold{y=11}$

$2)\ \left \{ {{2x+y=5} \atop {x-3y=6}} \right. \\\\\\\left \{ {{3(2x+y)=3(5)} \atop {x-3y=6}} \right. \\\\\\\left \{ {{6x+3y=15} \atop {x-3y=6}} \right. \\\\6x+3y+x-3y=15+6\\\\6x+x=21\\\\7x=21\\\\\frac{7x}{7} =\frac{21}{7} \\\\\bold{x=3}$

$\left \{ {{2x+y=5} \atop {x-3y=6}} \right. \\\\\\\left \{ {{2x+y=5} \atop {(-2)(x-3y)=(-2)(6)}} \right. \\\\\\\left \{ {{2x+y=5} \atop {-2x+6y=(-12)}} \right. \\\\\\2x+y+(-2x+6y)=5+(-12)\\\\2x+y-2x+6y=5-12\\\\y+6y=(-7)\\\\7y=(-7)\\\\\frac{7y}{7} =\frac{-7}{7} \\\\\bold{y=(-1)}$