Please help me with this math question!?

Question

What positive value of k would make the lines below parallel in the standard (x,y) coordinate plane?
kx+2y=8
18x+ky=12

Answer 1

-kx/2 = -18x/k
-k^2(x)= -36x
k^2 = 36
k = 6, -6

k=6, -6 because for the lines to be parallel the slopes have to be equal.

Answer 2

lines are parallel when their slopes are equal. Put the equations in the slope y intercept form: y = mx + b. The slope m is the number in front of the x.

kx + 2y = 8 yields y= (-k/2)x + 4 yields slope = -k/2

18x + ky = 12 yelds y = (-18/k)x + 12/k yields slope = -18/k

For parallel lines: -k/ 2 = -18/k

cross multiplying we get k^2 = 36.

Therefore k = +6 and -6 (two answers). The corresponding slopes will be +3 and -3.

Answer 3

For the lines to parallel, their slopes have to be equal.

First convert each one to y = mx + b, where m is the slope

1. 2y = 8 - kx, y = 4 - kx/2, so the slope is -k/2

2. ky = 12 - 18x, y = 12/y - 18x/k, so the slope is -18/k

Now set the two slopes to be equal, -k/2 = -18/k, which yields -k^2 = -36, or k = 6

Answer 4

6.

I got it this way:

kx +2y = 8
18x + ky = 12

2y = -kx + 8
ky = -18x + 12

y = -kx/2 + 4
y = -18x/k + 12

For the lines to be parallel, the slopes must be equal so:

-kx/2 = -18x/k

Get rid of the minus sign:

kx/2 = 18x/k

Multiply by 2:

kx = 36x/k

Multiply by k:

k^2 x = 36 x

Divide by x:

k^2 = 36

k = 6

Answer 5

2y = - k x + 8
y = (- k / 2).x + 4

ky = - 18 x + 12
y = ( - 18 / k).x + 12 / k

To be parallel:-
(- k/2) = (-18/k)
k/2 = 18/k
k² = 36
k = 6 (taking positive value)

Answer 6

18;k=l;2
k¨2=36
k=+ or-6 answer

Answer 7

the answer to K is 23

Answer 8

use linear method(elimination method)