k = -6
Step-by-step explanation:
The first equation: 2x + 3y = 6
The second equation: 4x – ky = 10
For two lines to be parallel to each other, the slope of both lines must be equal.
2x + 3y = 6
Rewritting in the slope-intercept form to get the slope:
3y = -2x + 6
y = -2x/3 + 6/3
y = -2x/3 + 2
4x – ky = 10
Rewritting in the slope-intercept form to get the slope:
ky = 4x - 10
y = 4x/k - 10
Equating both slope since they are equal:
-2x/3 = 4x/k
cross multiply:
-2xk = 12x
divide both sides by x:
-2k = 12
k = 12/-2
k = -6