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17 September, 23:26

Substitute - 3 for a and 8 for b in the given equations. Then, tell whether each equation is true or false.

The equation 5x - 7 (x - 1) = ax + b has excalty one solution (True or False)

The equation 3 (x - 5) - 7 = ax + b has no solution (True or False)

The equation 2 - 7x + 3 + 4x = ax + b has no solution (True or False)

The equation - 3 (x - 3) - 1 = ax + b has infinitely many solutions (True or False)

The equation - 5x + 2 + 2x + 4 = ax + b has infinitely many solutions (True or False)

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Answers (1)
  1. 18 September, 02:41
    0
    see below

    Step-by-step explanation:

    The equation 5x - 7 (x - 1) = ax + b has exactly one solution (True or False)

    Distribute the - 7 and substitute a and b

    5x - 7x+7 = - 3x+8

    -2x+7 = - 3x+8

    This has one solution because they are not the same line or parallel lines.

    True

    The equation 3 (x - 5) - 7 = ax + b has no solution (True or False)

    Distribute the 3 and substitute a and b

    3x-15 - 7 = - 3x+8

    3x-22 = - 3x+8

    The slopes are not the same so they are not parallel lines. It has one solution.

    False

    The equation 2 - 7x + 3 + 4x = ax + b has no solution (True or False)

    Substitute in a and b

    2 - 7x + 3 + 4x = - 3x + 8

    Combine like terms

    5 - 3x = - 3x+8

    The slopes are the same but the y intercepts are different. The lines will never intersect. They have no solutions

    True

    The equation - 3 (x - 3) - 1 = ax + b has infinitely many solutions (True or False)

    Distribute the - 3 and substitute a and b

    -3 (x - 3) - 1 = - 3x + 8

    -3x + 9 - 1 = - 3x + 8

    -3x+8 = - 3x+8

    This is the same line so it has infinite solutions

    True

    The equation - 5x + 2 + 2x + 4 = ax + b has infinitely many solutions (True or False)

    Substitute in a and b

    -5x + 2 + 2x + 4 = - 3x + 8

    -3x+6 = - 3x+8

    The slopes are the same but the y intercepts are different. These are parallel lines so they do not intersect. There are no solutions

    False
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