Answer
Fill in the blank is
empty set.
inconsistent system.
are parallel.
Work Step by Step
The given equations are.
$ 12x-21y=24 $ ... (1)
$ 4x-7y=7 $ ... (2)
Multiply equation (2) by $ -3 $.
$ -12x+21y=-21 $ ... (3)
Add equation (1) and (3).
$ 12x-12x-21y+21y=24-21 $
Add liker terms
$ 0=3 $
This is the false statement, which indicate the the solution set is empty.
And the linear system is inconsistent system.
In the graph we obtain two parallel lines.