Which of these graphs shows that the linear system y=−x+6 and 3x+3y=18 has an infinite number of solutions?(1 point)
Responses
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.
Image 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.
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.
Image 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.
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.
Image 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.
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.
Image 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.
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The first graph shows that the linear system y = -x + 6 and 3x + 3y = 18 has an infinite number of solutions.
The correct graph that shows that the linear system y=−x+6 and 3x+3y=18 has an infinite number of solutions is:
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.
To determine which graph shows that the linear system y = -x + 6 and 3x + 3y = 18 has an infinite number of solutions, we need to look for the graph where the two equations represent the same line, or where the lines are parallel and coincident.
Let's analyze each option:
Option A: This graph shows a downward slanting line passing through the points (-6, 0) and (0, -6). It does not represent the same line as 3x + 3y = 18.
Option B: This graph shows a downward slanting line passing through the points (0, 6) and (6, 0). It does not represent the same line as 3x + 3y = 18.
Option C: This graph shows two parallel lines. One solid downward slanting line passing through the points (0, 6) and (6, 0), and one dotted downward slanting line passing through the points (0, 4) and (4, 0). These lines are not coincident and do not represent the same line as 3x + 3y = 18.
Option D: This graph shows two intersecting lines. One solid downward slanting line passing through the points (0, 6) and (6, 0), and one dotted downward slanting line passing through the points (-6, 4) and (3, 3). These lines are not parallel and do not represent the same line as 3x + 3y = 18.
Based on the analysis, none of the given options represent the situation where the linear system has an infinite number of solutions.