find a value of k so that the following equations are consistent:
kx - 3y - 5 = 0
8x + y - 17 =0
kx + 2y -10 = 0
can k have more than one value satisfying this condition?

Question

amistre64 · Answer

kx = 3y+5

kx = -2y +10

amistre64 · Answer

0 = 5y -5

5 = 5y

y = 1

anonymous · Answer

but what about the 2nd equation?

amistre64 · Answer

kx = 8

k = 8/x  when you find x :)

amistre64 · Answer

8x +1 - 17 = 0

8x -16 = 0

8x = 16

x = 2

amistre64 · Answer

k = 4

anonymous · Answer

can't you just add all three equations together and solve for x in terms of k? I got x = 25/(2k+8)

amistre64 · Answer

add?   no,  you would need to use one of them as a "control" and subtract the other 2 from it if you were going that route

amistre64 · Answer

x + y = 0

2x + 3y = 0

3x +4y = 0 ???  nah

anonymous · Answer

okay that's what I confused myself on. thanks.

amistre64 · Answer

and since these are lines with different slopes, you cant have another value of "k" that would work.... thats just my gut feeling