Can this system of linear equations have infinite solutions?

Question

$ax_1 + bx_2 + 2x_3 = 1$

$x_1 + x_2 + x_3 = 1$

I'm fairly sure that I cannot, however my exam prep question seems to suggest that it might (perhaps it's poorly worded).

Answer 1

It can have infinitely many solutions (e.g. When $a=1, b=1$) and it can also have NO solution e.g. When $a=2, b=2$.

For the case $a=1, b=1$, the solution set is given by $(t,1-t,0)$, where $t$ is any real number.