One Solution, No Solution, or Many Solutions Quick Check%0D%0A3 of 53 of 5 Items%0D%0A%0D%0A%0D%0A%0D%0A%0D%0A%0D%0A%0D%0A%0D%0AQuestion%0D%0AWhich of these graphs shows that the linear system −2x+y=6 and 4x−2y=−12 has an infinite number of solutions?(1 point)%0D%0AResponses%0D%0A%0D%0A%0D%0AImage with alt text: A coordinate plane with 4 quadrants shows x and y axes ranging from negative 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 left parenthesis negative 3 comma 0 right parenthesis and left parenthesis 0 comma 6 right parenthesis. A solid upward slanting line with arrows at both ends, parallel to the dotted line, passes through origin.%0D%0A%0D%0A%0D%0AImage with alt text: A coordinate plane with 4 quadrants shows x and y axes ranging from negative 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 left parenthesis negative 3 comma 0 right parenthesis and left parenthesis 0 comma 6 right parenthesis.%0D%0A%0D%0A%0D%0AImage with alt text: A coordinate plane with 4 quadrants shows x and y axes ranging from negative 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 left parenthesis 0 comma negative 6 right parenthesis and left parenthesis 3 comma 0 right parenthesis.%0D%0A%0D%0A%0D%0AImage with alt text: A coordinate plane with 4 quadrants shows x and y axes ranging from negative 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 left parenthesis negative 3 comma 0 right parenthesis and left parenthesis 0 comma 6 right parenthesis. A dotted upward slanting line passes through the points left parenthesis 0 comma 6 right parenthesis and left parenthesis 1 comma 7 right parenthesis.%0D%0ASkip to navigation%0D%0A%0D%0A%0D%0A%0D%0AHighlight%0D%0AItem%0D%0A1%0D%0A, Fully Attempted.%0D%0AItem%0D%0A2%0D%0A, Fully Attempted.%0D%0AItem%0D%0A3%0D%0A, Fully Attempted.%0D%0AItem%0D%0A4%0D%0A, Unattempted.%0D%0AItem%0D%0A5%0D%0A, Unattempted.%0D%0APreviousNext

Question

One Solution, No Solution, or Many Solutions Quick Check%0D%0A3 of 53 of 5 Items%0D%0A%0D%0A%0D%0A%0D%0A%0D%0A%0D%0A%0D%0A%0D%0AQuestion%0D%0AWhich of these graphs shows that the linear system −2x+y=6 and 4x−2y=−12 has an infinite number of solutions?(1 point)%0D%0AResponses%0D%0A%0D%0A%0D%0AImage with alt text: A coordinate plane with 4 quadrants shows x and y axes ranging from negative 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 left parenthesis negative 3 comma 0 right parenthesis and left parenthesis 0 comma 6 right parenthesis. A solid upward slanting line with arrows at both ends, parallel to the dotted line, passes through origin.%0D%0A%0D%0A%0D%0AImage with alt text: A coordinate plane with 4 quadrants shows x and y axes ranging from negative 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 left parenthesis negative 3 comma 0 right parenthesis and left parenthesis 0 comma 6 right parenthesis.%0D%0A%0D%0A%0D%0AImage with alt text: A coordinate plane with 4 quadrants shows x and y axes ranging from negative 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 left parenthesis 0 comma negative 6 right parenthesis and left parenthesis 3 comma 0 right parenthesis.%0D%0A%0D%0A%0D%0AImage with alt text: A coordinate plane with 4 quadrants shows x and y axes ranging from negative 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 left parenthesis negative 3 comma 0 right parenthesis and left parenthesis 0 comma 6 right parenthesis. A dotted upward slanting line passes through the points left parenthesis 0 comma 6 right parenthesis and left parenthesis 1 comma 7 right parenthesis.%0D%0ASkip to navigation%0D%0A%0D%0A%0D%0A%0D%0AHighlight%0D%0AItem%0D%0A1%0D%0A, Fully Attempted.%0D%0AItem%0D%0A2%0D%0A, Fully Attempted.%0D%0AItem%0D%0A3%0D%0A, Fully Attempted.%0D%0AItem%0D%0A4%0D%0A, Unattempted.%0D%0AItem%0D%0A5%0D%0A, Unattempted.%0D%0APreviousNext

Answer 1

The correct graph that shows that the linear system has an infinite number of solutions is the first one described in the response. It is the one with two parallel lines, one dotted and one solid, both upward slanting and passing through the points (-3, 0) and (0, 6).

Answer 2

The graph that shows that the linear system −2x+y=6 and 4x−2y=−12 has an infinite number of solutions is the first image described in the question. It shows a coordinate plane with two parallel lines. The dotted line passes through the points (-3, 0) and (0, 6), and the solid line is parallel to the dotted line and passes through the origin.

Answer 3

To determine which graph shows that the linear system -2x + y = 6 and 4x - 2y = -12 has an infinite number of solutions, we need to understand the properties of the system of equations.

The system of equations has an infinite number of solutions when the two equations represent the same line. This means that the lines are either identical or coincide.

Let's analyze each graph to see if it fits these criteria:

Graph 1:
This graph shows two parallel lines. One line passes through the points (-3, 0) and (0, 6), while the other line is parallel to the first line and passes through the origin. These lines are not identical or coincident, so they do not represent an infinite number of solutions.

Graph 2:
This graph shows an upward-slanting line passing through the points (-3, 0) and (0, 6). It does not represent the second equation, so it is not a solution to the system.

Graph 3:
This graph shows an upward-slanting line passing through the points (0, -6) and (3, 0). It does not represent the first equation, so it is not a solution to the system.

Graph 4:
This graph shows two intersecting lines. One line passes through the points (-3, 0) and (0, 6), while the other line passes through the points (0, 6) and (1, 7). These lines are not identical or coincident, so they do not represent an infinite number of solutions.

Based on this analysis, none of the given graphs show that the linear system has an infinite number of solutions.