SOLUTION: Given the following system of equations, what positive value of k would make the lines below parallel? kx+2y=8 and 18x+ky=12 Thank you!

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Question 1147938: Given the following system of equations, what positive value of k would make the lines below parallel? kx+2y=8 and 18x+ky=12
Thank you!
Found 3 solutions by MathLover1, greenestamps, ikleyn:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
given:
kx%2B2y=8
18x%2Bky=12
find: what positive value of k would make the lines below parallel?

recall that parallel line have same slope
so, write both equations in slope intercept form
kx%2B2y=8 ......solve for y
2y=-kx%2B8 ...both sides divide by 2
y=-%28k%2F2%29x%2B4 => slope is -%28k%2F2%29

18x%2Bky=12.....take same steps as above
ky=-18x%2B12
y=-%2818%2Fk%29x%2B12%2Fk => slope is -%2818%2Fk%29

if slopes are same , we have
-%28k%2F2%29=-%2818%2Fk%29..........solve for k, first cross multiply
-%28k%29k=-%2818%292
-k%5E2=-36......both sides multiply by -1
k%5E2=36
k=sqrt%2836%29
highlight%28k=6%29=>positive value of k that we need

and, your lines are
6x%2B2y=8
18x%2B6y=12
or in slope intercept form
y=-%286%2F2%29x%2B4=>y=-3x%2B4
y=-%2818%2F6%29x%2B12%2F6 =>y=-3x%2B2

proof with a graph:
+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+-3x%2B4%2C+-3x%2B2%29+

as you can see, the lines are parallel if highlight%28k=6%29



Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The graphs of Ax+By=M and Cx+Dy=N are parallel if, and only if,

A/B = C/D

or, alternatively,

A/C = B/D

Using the first ratio, we have

k%2F2+=+18%2Fk
k%5E2+=+36
k+=+6 OR k+=+-6

Of course we choose k=6 for the answer, because the question asks for a positive value.

Answer by ikleyn(52787) About Me  (Show Source):
You can put this solution on YOUR website!
.
Given the following system of equations, what positive value of k would make the lines below parallel? kx+2y=8 and 18x+ky=12
Thank you!
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Notice that the problem could be formulated in  MUCH SHORTER way  by omitting all the words starting from the very first word

and ending by the "comma" symbol, without any loss in its meaning.


So, these words in the problem formulation (underlined by me) are absolutely useless, unnecessary and excessive in the condition (!)


For the author of a Math problem, it is a "great sin" to introduce useless, unnecessary and excessive words into the condition . . .


At the normal/regular editorial environment, such a formulation would never had a chance to be issued publicly (!)