Question

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.

Answer 1

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

Explanation:

Answer 2

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)