y=5x-4 (1,1) , y-4x+1=0 (1,7) Plug a few points into the original equations and check to show that the system of

Question

equations has no solution. Explain your work

Answer 1

Using the first equation y = 5x - 4, we can plug in the point (1,1):

1 = 5(1) - 4
1 = 5 - 4
1 = 1

This checks out, as (1,1) is a point on the line defined by y = 5x - 4.

Using the second equation y - 4x + 1 = 0, we can plug in the point (1,7):

7 - 4(1) + 1 = 0
7 - 4 + 1 = 0
4 = 0

This shows that (1,7) is not a point on the line defined by y - 4x + 1 = 0.

Therefore, since the two points are not on the same line, the system of equations has no solution.