+0  
 
0
81
3
avatar

For what value of $k$ are the lines $2x + 3y = 4k$ and $x - 2ky = 7$ parallel? Express your answer as a common fraction.

 Aug 7, 2022
 #1
avatar+113 
+1

I got this in GeoGebra

 Aug 7, 2022
 #2
avatar+2446 
0

Multiplying the second equation by 2 gives us \(2x - 4ky = 14\)

 

If the equations are parallel, they never intersect, meaning the system has no solutions.

 

So we have the equation \(3y = -4ky\), and solving the equation gives us \(k = \color{brown}\boxed{-{3 \over 4}}\) 

 Aug 7, 2022
 #3
avatar+33151 
+1

I'd do it as follows:

 

 Aug 8, 2022

17 Online Users