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sqdancefan

Answer:

  (d)  2x +y = 8

Step-by-step explanation:

The answer choices are shown in "standard form," so the comparison to the given equation is easier if it is written in standard form. Add 2x to both sides:

  2x +y = 5 . . . . . . given equation in standard form

The other equation in a system with no solution will look like this, but will have a different constant:

  2x +y = 8 . . . . . . does not intersect the given equation

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Additional comment

All of the other equations shown will intersect the given equation. One way to show this is to use the given equation to substitute for y in the answer choices:

  a: 2x -(-2x+5) = 8   ⇒   6x -5 = 8 . . . one solution: x=13/6

  b: x +2(-2x+5) = 8   ⇒   -3x +10 = 8 . . . one solution: x=2/3

  c: x -2(-2x+5) = 8   ⇒   5x -10 = 8 . . . one solution: x=18/5

  d: 2x +(-2x+5) = 8   ⇒   5 = 8 . . . no solution

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