is y=5x-4 and y=5x-5 a one solution, no solution or infinitely many solution

Answer 1

(1) y = 5x - 4

(1) y = 5x - 5

Subtracting the first equation from the second equation yields

(3) 0 = 1

Clearly there is no possible of x that will make equation (3) a true statement. So if the goal is to make a list of all values of x that make the two original equations true at the same time, the the answer is that no such x exists.

Answer 2

This one is convenient since both equations are solved for Y. Using substitution, 5x-4=5x-5. Subtract 5x from both sides and we have 4=5. Since this is not true, there is no solution.

Alternatively, we can recognize these as parallel lines and see that they have different y-intercepts. So they will never cross, and there is no solution.