One Solution, No Solution, or Many Solutions Quick Check%0D%0A4 of 54 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 y=−x+6 and 3x+3y=18 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 intersecting lines are plotted on the plane. A solid downward slanting line with arrows at both ends passes through the points left parenthesis 0 comma 6 right parenthesis and left parenthesis 6 comma 0 right parenthesis. A dotted downward slanting line with arrows at both ends passes through the points left parenthesis negative 6 comma 4 right parenthesis and left parenthesis 3 comma 3 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 parallel lines are plotted on the plane. A solid downward slanting line with arrows at both ends passes through the points left parenthesis 0 comma 6 right parenthesis and left parenthesis 6 comma 0 right parenthesis. A dotted downward slanting line with arrows at both ends passes through the points left parenthesis 0 comma 4 right parenthesis and left parenthesis 4 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. A line is plotted on the plane. A downward slanting line with arrows at both ends passes through the points left parenthesis negative 6 comma 0 right parenthesis and left parenthesis 0 comma negative 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. A downward slanting line with arrows at both ends passes through the points left parenthesis 0 comma 6 right parenthesis and left parenthesis 6 comma 0 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%0A4 of 54 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 y=−x+6 and 3x+3y=18 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 intersecting lines are plotted on the plane. A solid downward slanting line with arrows at both ends passes through the points left parenthesis 0 comma 6 right parenthesis and left parenthesis 6 comma 0 right parenthesis. A dotted downward slanting line with arrows at both ends passes through the points left parenthesis negative 6 comma 4 right parenthesis and left parenthesis 3 comma 3 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 parallel lines are plotted on the plane. A solid downward slanting line with arrows at both ends passes through the points left parenthesis 0 comma 6 right parenthesis and left parenthesis 6 comma 0 right parenthesis. A dotted downward slanting line with arrows at both ends passes through the points left parenthesis 0 comma 4 right parenthesis and left parenthesis 4 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. A line is plotted on the plane. A downward slanting line with arrows at both ends passes through the points left parenthesis negative 6 comma 0 right parenthesis and left parenthesis 0 comma negative 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. A downward slanting line with arrows at both ends passes through the points left parenthesis 0 comma 6 right parenthesis and left parenthesis 6 comma 0 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 graph that shows the linear system y=−x+6 and 3x+3y=18 has an infinite number of solutions is the first one described in the prompt. It is the image of a solid downward slanting line with arrows at both ends passing through the points (0, 6) and (6, 0), and a dotted downward slanting line with arrows at both ends passing through the points (-6, 4) and (3, 3).

Answer 2

The graph that shows the linear system y=−x+6 and 3x+3y=18 has an infinite number of solutions is the first one. It is the image with a solid downward slanting line and a dotted downward slanting line intersecting on the coordinate plane.

Answer 3

To determine which of the graphs shows that the linear system y = -x + 6 and 3x + 3y = 18 has an infinite number of solutions, we need to understand the concept of intersecting lines.

When two lines intersect, they have exactly one common point of intersection. If the system of equations representing the lines has a unique solution, then the graphs will have only one point of intersection.

However, if the two lines are coincident or overlapping, they have an infinite number of points in common and will have infinitely many solutions to the system of equations.

Now let's examine the given graphs:

Graph 1: This graph shows two intersecting lines. One line is solid and passes through the points (0, 6) and (6, 0), while the other line is dotted and passes through the points (-6, 4) and (3, 3).

Graph 2: This graph shows two parallel lines. One line is solid and passes through the points (0, 6) and (6, 0), while the other line is dotted and passes through the points (0, 4) and (4, 0).

Graph 3: This graph shows a single line passing through the points (-6, 0) and (0, -6).

Graph 4: This graph shows a single line passing through the points (0, 6) and (6, 0).

Based on our understanding, the graph that represents an infinite number of solutions is Graph 1. Since the two lines in Graph 1 intersect at infinitely many points, it indicates that the system of equations has an infinite number of solutions.

Therefore, the correct answer is Graph 1.