Question

L1: 2x+4y-1=0
L2: 5x+y-15=0
L3: x+2y+3=0

a.Distance between L1 and L3
b.General equation of line with slope equal to one-fifth the slope of L2 and which passes through the intersection of L1 and L2?
c. What is the general equation of the line perpendicular to L1 and which passes through the x intercept of L2?

Answer 1

Lets find the intersection of L1 and L2:
2x + 4y -1 = 0
5x + y - 15=0 Using the elimination and transposing.
multiply the 2nd (L2) equation by -4 you will get: -20x -4y + 60 = 0
2x + 4y = 1
-20x - 4y = -60
----------------adding the equations
-18x = -59
x=59/18 substituting and then solving for y
59/9 + 4y = 1
4y =1 -59/9=-50/9
y = -59/36
Intersection at (59/18, -59/36)

I am troubled by this odd=ball values of x and y, but all problems don't have to have "neat" solutions.

Please review the above and if I have made no mistakes, we can continue with the solution of part b.
a few moments ago