# Sample quiz on consistency vs inconsistency Main home here.

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.
$b=6,k=2$
$b=3,k=4$
$b=4,k=3$
$b=2,k=6$