Given a system of equations:
$x+2y+2z=b_1$
$5x+y+3z=b_2$
Which of the following is true regarding its solutions
- The system has a unique solution for any given $b_1$ and $b_2$
- The system will have infinitely many solutions for any given $b_1$ and $b_2$
- Whether or not a solution exists depends on the given $b_1$ and $b_2$
- The system would have no solution for any values of $b_1$ and $b_2$