How are these two lines coincident?
1) r=(1,7)+s(2,5)
2) x=4t+3 y=10t+12
1)
x = 1 + 2 s or s = (x-1)/2
y = 7 + 5 s
y = 7 +(5/2)(x-1)
2y = 14 + 5 x - 5
5 x - 2 y = -9
now where does that hit 2) ?
t = (x-3)/4
so
y = (10/4)(x-3) + 12
4 y = 10 x - 30 + 48
10 x - 4 y = -18
so we have two equations
5 x - 2 y = -9
10 x - 4 y = -18
BUT
THEY ARE the SAME
they are coincident everywhere on either.