determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. Find all solutions whenever they exist.x+3y=93x-y=7

[tex] \left \{ {{x+3y=9~(3)} \atop {3x-y=7(-1)}} \right. \\
\\ \left \{ {{3x+9y=27} \atop {-3x+y=-7}} \right. \\ \\10y=20\\
\\y= \frac{20}{10} \\y=2[/tex][tex]x+3y=9\\x=9-3y\\x=9-3.2\\x=3[/tex][tex]S=\{3,2\}[/tex]One solution.

[tex]x+3y=9\\
3x-y=7\ / \cdot 3\\
\\
x+3y=9\\
9x-3y=21\\
\\
10x=30\ /:10\\
x=3\\
\\
x+3y=9\\
3+3y=9\\
3y=6\\
y=2\\
one\ solution - (3;2)[/tex]