A system of equations is given below. y = 2x + 1/4 and 2x - 1/4

Which of the following statements best describes the two lines?

They have the same slope but different y-intercepts, so they have no solution.
They have the same slope but different y-intercepts, so they have one solution. They have different slopes but the same y-intercept, so they have no solution.
They have different slopes but the same y-intercept, so they have one solution.

As the slopes are the same (2) but the y-intercepts are different, it means that the straights are parallel. Parallel equations have no solution as the straights don't intercept each other.

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Cetacea Cetacea · Answer 2 · 2022-01-18T11:31:38+01:00

Answer: They have the same slope but different y-intercepts, so they have no solution.

The given equations are [tex]y=2x+\frac{1}{4}[/tex] and [tex]y=2x-\frac{1}{4}[/tex].

We compare them with y = mx + b.

So the slope of both of them is m=2.

y-intercept for the first one is = b = 1/4

y-intercept for the second one is = b = -1/4

Hence, the lines are parallel and will never meet and will have no solution.

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