x = 1

y = 2

решение ниже

Verified answer

[tex]\boxed{Otvet:x=1,y=2}[/tex]

Метод подстановки:

[tex]\displaystyle\left \{ {{x+3y=7} \atop {7x-3y=1}} \right. \Leftrightarrow \left \{ {{x=7-3y} \atop {7x-3y=1}} \right.[/tex]

[tex]7(7-3y)-3y=1\\(7*7-7*3y)-3y=1\\49-21y-3y=1\\49-24y=1\\-24y=1-49\\-24y=-48|:-24\\y=2[/tex]

[tex]x+3*2=7\\x+6=7\\x=7-6\\x=1[/tex]

Метод сложения:

[tex]\displaystyle\left \{ {{x+3y=7} \atop {7x-3y=1}} \right.[/tex]

[tex](x+3y)+(7x-3y)=7+1\\x+3y+7x-3y=8\\x+7x=8\\8x=8|:8\\x=1[/tex]

[tex]1+3y=7\\3y=8-1\\3y=6|:3\\y=2[/tex]