# ANSWER WITH SOLUTION: Find the value of K so that Kx-3y=5 and 5x-6y=8 will be parallel and perpendicular

1
by analyticgeometry

• Brainly User
2016-01-29T13:56:41+08:00
Transform the equations to slope-intercept form, y = mx + b; m=slope

1) For parallel equations, the slopes must be equal.
Equation 1:
5x - 6y = 8
- 6y = - 5x + 8
- 6y/-6  = -5x/-6 + 8/-6
y = 5x/6 - 4/3
m = 5/6

Equation 2:
kx - 3y = 5
- 3y = -kx + 5
- 3y/-3  = -kx/-3 + 5/-3
y = kx/3 - 5/3
m = k/3

Solve for k:
m = 5/6
k/3 = 5/6
6k = (3) (5)
6k = 15
6k/6 = 15/6
k = 5/2

Therefore, Equation 2 is:
5x/2 - 3y = 5     LCD: 2
2 (5x/2 - 3y = 5)2
5x - 6y = 10

Slope-intercept form:
-6y = -5x + 10
-6y/-6 = -5x/-6 + 10/-6
y = 5x/6 - 5/3
m = 5/6   (True)

2)  For perpendicular equations, the product of the slopes of the two equations is -1.
Equation 1:
m = 5/6

Equation 2:
m = -6/5

Solve for k:
k/3 = -6/5
5k = (3) (-6)
5k = -18
5k/5 = -18/5
k = -18/5

Therefore, to make the equations perpendicular, Equation 2 is:
kx - 3y = 5
-18x/5 - 3y = 5       LCD: 5
5 (-18x/5 - 3y = 5) 5
-18x - 15y = 25

Slope-intercept form:
-15y = 18x + 25
-15y/-15 = 18x/-15 + 25/-15
y = -6x/5 - 5/3
m = -6/5    (True)

ANSWER:  To make the equations parallel, k = 5/2.
To make the equations perpendicular, k = -18/5