Question

x+8y=7 (1)
x=3-8y (2) solve the system of equations

Answer 1

substitute x=3-8y to x+8y=7
it will be
3-8y+8y=7
from this you can't find y, so you cant find x as well. therefore the system doesn't have unique solution

Answer 2

A better way to approach this question for the purpose of understanding is to first make x the subject of equation 1
So x = 7 - 8y
Both equations now have a gradient of -8.
Their respectice y intercepts or constants are, however, different, which helps you to see that the lines are parallel and meet at infinity (or in layman's terms never meet at all!)
OK this has not answered the question as you posed it but if you follow dindact's method, my method will then help you to see what happens to the equations.