Which system of equations below has no solution?

y = 4x + 5 and y = 4x-5

y = 4x + 5 and 2y = 8x + 10

y = 4x + 5 and y =

x+5

y = 4x + 5 and y = 8x + 10

y = 4x + 5 and y = 4x - 5

Step-by-step explanation:

(1) y = 4x + 5 and (2) y = 4x - 5

substitute (1) to (2):

4x + 5 = 4x - 5 subtract 4x from both sides

5 = - 5 FALSE (no solution)

(1) y = 4x + 5 and (2) 2y = 8x + 10

substitute (1) to (2):

2 (4x + 5) = 8x + 10 divide both sides by 2

4x + 5 = 4x + 5 subtract 4x from both sides

5 = 5 TRUE (infinitely many solutions)

(1) y = 4x + 5 and (2) y = x + 5

substitute (1) to (2):

4x + 5 = x + 5 subtract 5 from both sides

4x = x subtract x from both sides

3x = 0 divide both sides by 3

x = 0

Put it to (2):

y = 0 + 5 = 5

One solution (0, 5)

(1) y = 4x + 5 and (2) y = 8x + 10

substitute (1) to (2):

4x + 5 = 8x + 10 subtract 5 from both sides

4x = 8x + 5 subtract 8x from both sides

-4x = 5 divide both sides by (-4)

x = - 1.25

Put it to (1):

y = 4 (-1.25) + 5 = - 5 + 5 = 0

One solution (-1.25, 0)