Question

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=9
3x-y=7

Answer 1

$\left \{ {{x+3y=9~(3)} \atop {3x-y=7(-1)}} \right. \\ \\ \left \{ {{3x+9y=27} \atop {-3x+y=-7}} \right. \\ \\10y=20\\ \\y= \frac{20}{10} \\y=2$

$x+3y=9\\x=9-3y\\x=9-3.2\\x=3$

$S=\{3,2\}$

One solution.

Answer 2

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