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Given a system of equations:

$x+2y+2z=b_1$

$5x+y+3z=b_2$

Which of the following is true regarding its solutions

1. The system has a unique solution for any given $b_1$ and $b_2$
2. The system will have infinitely many solutions for any given $b_1$ and $b_2$
3. Whether or not a solution exists depends on the given $b_1$ and $b_2$
4. The system would have no solution for any values of $b_1$ and $b_2$

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