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!

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)   (Show Source): You can put this solution on YOUR website!
given:

find: what positive value of would make the lines below parallel?

recall that parallel line have
so, write both equations in slope intercept form
......solve for
...both sides divide by
=> slope is

.....take same steps as above

=> slope is

if are , we have
..........solve for , first cross multiply

......both sides multiply by

=>positive value of that we need

and, your lines are

or in slope intercept form
=>
=>

proof with a graph:

as you can see, the lines are parallel if

Answer by greenestamps(13200)   (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

OR

Of course we choose k=6 for the answer, because the question asks for a positive value.
Answer by ikleyn(52794)   (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!
~~~~~~~~~~~~~~~

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 (!)

RELATED QUESTIONS
What positive of k would make the lines below parallel. {{{ kx+2y=8 }}} {{{ 18x+ky=12... (answered by ewatrrr)
find the value of k for which the following system of equations has no solution... (answered by Tatiana_Stebko)
Find k if the following system of equations has infinite solutions kx + 3y = k � 3 (answered by jim_thompson5910)
what is k if the following system of equations has a unique solution: 2x+(k-1)y=6... (answered by stanbon)
for what values of k is the system of equations kx+3y=k-2,12x+ky=k inconsistent... (answered by Edwin McCravy)
Solve the system of equations kx + 2y = 1 and 2x + ky = -2 as k takes all real values... (answered by richwmiller)
find the value of k that will make the lines 2x + y = 3 and kx + y = -1 parallel (answered by tutor_paul)
Hello I need help on this problem, please! Solve the system of equations kx + 2y = 1 and (answered by TimothyLamb)
find the value of k so that the two given lines will be parallel: (k+2)x-5y=8 and... (answered by robertb)