Show the two lines (x/2-1/2)=(y/3-2/3)=(z/4-3/4) and (x/5-4/5)=z intersect.find the point of intersection of these lines

Answer 1

subbing the 2nd into the first:
x/2 - 1/2 = z/4 - 3/4
x/2 - 1/2 = (1/4)(x/5-4/5) - 3/4
times 4
2x - 2 = (x/5 - 4/5) - 3
times 5
10x - 10 = x - 4 - 15
9x = -9
x = -1

into z = x/5 - 4/4 = -1/5 - 4/5 = -1
z = -1

lastly
y/3 - 2/3 = z/4 - 3/4
y/3 - 2/3 = -1/4-3/4
y/3 - 2/3 = -1
times 3
y - 2 = -3

y = -1

they intersect at (-1, -1, -1)