Systems of Linear Equations Unit Test
6 of 146 of 14 Items
Question
Which of these graphs shows that the linear system 3x+2y=12 and 6x+4y=24 has an infinite number of solutions?(1 point)
Responses
1) 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 downward slanting line with arrows at both ends passes through the points left parenthesis negative 4 comma 0 right parenthesis and left parenthesis 0 comma negative 6 right parenthesis. A solid downward slanting line with arrows at both ends passes through the points left parenthesis 0 comma 6 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 dotted downward slanting line with arrows at both ends passes through the points left parenthesis negative 4 comma 0 right parenthesis and left parenthesis 0 comma negative 6 right parenthesis. A solid downward slanting line with arrows at both ends passes through the points left parenthesis 0 comma 6 right parenthesis and left parenthesis 4 comma 0 right parenthesis.
2) 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 10 comma 9 right parenthesis and left parenthesis negative 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. A line is plotted on the plane. A downward slanting line with arrows at both ends passes through the points left parenthesis negative 10 comma 9 right parenthesis and left parenthesis negative 4 comma 0 right parenthesis.
3) 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 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. 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 4 comma 0 right parenthesis.
4) 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 passes through the points left parenthesis negative 6 comma 3 right parenthesis and left parenthesis negative 4 comma 0 right parenthesis. A dotted upward slanting line passes through the points left parenthesis 0 comma negative 6 right parenthesis and left parenthesis 6 comma 4 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 passes through the points left parenthesis negative 6 comma 3 right parenthesis and left parenthesis negative 4 comma 0 right parenthesis. A dotted upward slanting line passes through the points left parenthesis 0 comma negative 6 right parenthesis and left parenthesis 6 comma 4 right parenthesis.
1) 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 downward slanting line with arrows at both ends passes through the points left parenthesis negative 4 comma 0 right parenthesis and left parenthesis 0 comma negative 6 right parenthesis. A solid downward slanting line with arrows at both ends passes through the points left parenthesis 0 comma 6 right parenthesis and left parenthesis 4 comma 0 right parenthesis.
This graph shows that the linear system has an infinite number of solutions because the two lines are parallel and will intersect at every point, indicating an infinite number of solutions.