Question

Which system of equations below has no solution?

Answer 1

Answer:

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)