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A system of equations is given below. y = negative 2 x + one-fourth and y = negative 2 x minus one-fourth 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.

User Sruthi J
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2 Answers

2 votes

Answer:

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

Explanation:

User Anna Krogager
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6.6k points
4 votes

Answer:

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

Explanation:

The slope is the coefficient of x. In both cases, it is -2, so the lines have the same slope. (This eliminates the last two answer choices.)

The added constants are different for the two lines, so they have different y-intercepts. This means the lines are parallel and do not intersect.

A "solution" to the system of equations is a point (x, y) that satisfies both equations. Since the lines have no points in common, there are no solutions. (matches the first answer choice)

User Abhi
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6.8k points
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