Sample quiz on consistency vs inconsistency
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1. If two lines have the same slope and the same $y$-intercept, they are said to be $\cdots$?
   
   parallel
   perpendicular
   coincident
   inconsistent
   
2. If two lines have the same slope but different $y$-intercepts, then they are $\cdots$
   
   parallel
   perpendicular
   inconsistent
   consistent
3. If two lines have different slopes but the same $y$-intercepts, then $\cdots$
   
   they can't intersect
   they always intersect
   they sometimes intersect
   they only intersect at $(0,0)$
4. How many solutions does the linear system $2x+3y=8,~4x+6y=-16$ have?
   
   $1$
   $0$
   infinitely many
   about a million
5. How many solutions does the linear system $-2x+5y=9,~2x-5y=-9$ have?
   
   $0$
   $1$
   infinitely many
   about a million
6. Given the linear system $2x+3y=8,~kx+6y=16$, find the value of $k$ for which there are infinitely many solutions.
   
   $k=4$
   $k=1$
   $k=3$
   $k=2$
7. Given the linear system $2x+3y=8,~4x+6y=c$, find the value of $c$ for which there are infinitely many solutions.
   
   $c=4$
   $c=8$
   $c=16$
   $c=32$
8. Given the linear system $2x+3y=8,~4x+ky=16$, find the value of $k$ so that the system is coincident.
   
   $k\neq 0$
   $k\neq 4$
   $k=4$
   $k=6$
9. Given the linear system $2x+3y=8,~4x+6y=c$, find a restriction on $c$ so that the system is inconsistent.
   
   $c\neq 32$
   $c\neq 16$
   $c\neq 8$
   $c\neq 4$
10. Given the linear system $2x+by=8,~kx+6y=16$, find appropriate choices for $b,k$ that will ensure consistency.
    
    $b=6,k=2$
    $b=3,k=4$
    $b=4,k=3$
    $b=2,k=6$