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29 September, 07:34

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

+5
Answers (1)
  1. 29 September, 11:28
    0
    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)
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