How are these two lines coincident?

Question

1) r=(1,7)+s(2,5)

2) x=4t+3 y=10t+12

Answer 1

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.