Question

Which of these graphs shows that the linear system −2x+y=6 and 4x−2y=−12 has an infinite number of solutions?(1 point)

A coordinate plane with 4 quadrants shows x and y axes ranging from -10 to 10 in unit increments. A line is plotted on the plane. An upward slanting line with arrows at both ends passes through the points (-3, 0) and (0, 6).

A coordinate plane with 4 quadrants shows x and y axes ranging from -10 to 10 in unit increments. Two intersecting lines are plotted on the plane. A solid upward slanting line with arrows at both ends passes through the points (-3, 0) and (0, 6). A dotted upward slanting line passes through the points (0, 6) and (1, 7).

A coordinate plane with 4 quadrants shows x and y axes ranging from -10 to 10 in unit increments. A line is plotted on the plane. An upward slanting line with arrows at both ends passes through the points (0, -6) and (3, 0).

A coordinate plane with 4 quadrants shows x and y axes ranging from -10 to 10 in unit increments. Two parallel lines are plotted on the plane. A dotted upward slanting line with arrows at both ends passes through the points (-3, 0) and (0, 6). A solid upward slanting line with arrows at both ends, parallel to the dotted line, passes through origin.

Answer 1

[AI-generated answer — Bot GPT 3.5]

The correct option is:

A coordinate plane with 4 quadrants shows x and y axes ranging from -10 to 10 in unit increments. Two intersecting lines are plotted on the plane. A solid upward slanting line with arrows at both ends passes through the points (-3, 0) and (0, 6). A dotted upward slanting line passes through the points (0, 6) and (1, 7).

This is because for a system of equations to have an infinite number of solutions, the two equations must represent the same line. In the given option, the solid line and the dotted line intersect at (0,6), indicating that they are the same line. Therefore, this option represents a linear system with an infinite number of solutions.

Answer 2

are you sure?

Answer 3

[AI-generated answer — Bot GPT 3.5]

I apologize for the confusion. You are correct; the previous answer was incorrect. Let me provide the correct response:

The graph that shows that the linear system −2x+y=6 and 4x−2y=−12 has an infinite number of solutions is:

A coordinate plane with 4 quadrants shows x and y axes ranging from -10 to 10 in unit increments. Two parallel lines are plotted on the plane. A dotted upward slanting line with arrows at both ends passes through the points (-3, 0) and (0, 6). A solid upward slanted line with arrows at both ends, parallel to the dotted line, passes through the origin.

This option represents the linear system with an infinite number of solutions because the two lines are parallel and have the same slope. Since the slopes are equal, the lines will never intersect, indicating an infinite number of solutions.