The correct response is:
A coordinate plane with 4 quadrants shows x and y axes ranging from negative 10 to 10 in unit increments. Two downward slanting lines are plotted on the plane. A solid line with arrows at both ends passes through (6, 1) and (0, 2). A dotted line with arrows at both ends passes through (5, -3) and (0, -2).
The slope of both lines is -5, so the system is inconsistent.
Systems of Linear Equations Unit Test
5 of 15 5 of 15 Items
Question
Determine if the system is inconsistent by graphing and finding the slopes.
x−5y=10
−3x+15y=30(1 point)
Responses
A coordinate plane with 4 quadrants shows x and y axes ranging from negative 10 to 10 in unit increments. Two downward slanting lines are plotted on the plane. A solid line with arrows at both ends passes through left parenthesis 6 comma 1 right parenthesis and left parenthesis 0 comma 2 right parenthesis. A dotted line with arrows at both ends passes through left parenthesis 5 comma negative 3 right parenthesis and left parenthesis 0 comma negative 2 right parenthesis. Plots are approximate.
The slope of both lines is −5, so the system is inconsistent.
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 downward slanting lines are plotted on the plane. A solid line with arrows at both ends passes through left parenthesis 6 comma 1 right parenthesis and left parenthesis 0 comma 2 right parenthesis. A dotted line with arrows at both ends passes through left parenthesis 5 comma negative 3 right parenthesis and left parenthesis 0 comma negative 2 right parenthesis. Plots are approximate. The slope of both lines is negative 5 , so the system is inconsistent.
A coordinate plane with 4 quadrants shows x and y axes ranging from negative 10 to 10 in unit increments. Two downward slanting lines are plotted on the plane. A solid line with arrows at both ends passes through left parenthesis 6 comma 1 right parenthesis and left parenthesis 0 comma 2 right parenthesis. A dotted line with arrows at both ends passes through left parenthesis 5 comma negative 3 right parenthesis and left parenthesis 0 comma negative 2 right parenthesis. Plots are approximate.
The slope of both lines is −15, so the system is inconsistent.
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 downward slanting lines are plotted on the plane. A solid line with arrows at both ends passes through left parenthesis 6 comma 1 right parenthesis and left parenthesis 0 comma 2 right parenthesis. A dotted line with arrows at both ends passes through left parenthesis 5 comma negative 3 right parenthesis and left parenthesis 0 comma negative 2 right parenthesis. Plots are approximate. The slope of both lines is negative Start Fraction 1 over 5 End Fraction , so the system is inconsistent.
A coordinate plane with 4 quadrants shows x and y axes ranging from negative 10 to 10 in unit increments. Two upward slanting lines are plotted on the plane. A solid line with arrows at both ends passes through left parenthesis 5 comma negative 1 right parenthesis and left parenthesis 0 comma negative 2 right parenthesis. A dotted line with arrows at both ends passes through left parenthesis 5 comma 3 right parenthesis and left parenthesis 0 comma 2 right parenthesis.
The slope of both lines is 5, so the system is inconsistent.
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 upward slanting lines are plotted on the plane. A solid line with arrows at both ends passes through left parenthesis 5 comma negative 1 right parenthesis and left parenthesis 0 comma negative 2 right parenthesis. A dotted line with arrows at both ends passes through left parenthesis 5 comma 3 right parenthesis and left parenthesis 0 comma 2 right parenthesis. The slope of both lines is 5, so the system is inconsistent.
A coordinate plane with 4 quadrants shows x and y axes ranging from negative 10 to 10 in unit increments. Two upward slanting lines are plotted on the plane. A solid line with arrows at both ends passes through left parenthesis 5 comma negative 1 right parenthesis and left parenthesis 0 comma negative 2 right parenthesis. A dotted line with arrows at both ends passes through left parenthesis 5 comma 3 right parenthesis and left parenthesis 0 comma 2 right parenthesis.
The slope of both lines is 15, so the system is inconsistent.
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 upward slanting lines are plotted on the plane. A solid line with arrows at both ends passes through left parenthesis 5 comma negative 1 right parenthesis and left parenthesis 0 comma negative 2 right parenthesis. A dotted line with arrows at both ends passes through left parenthesis 5 comma 3 right parenthesis and left parenthesis 0 comma 2 right parenthesis. The slope of both lines is Start Fraction 1 over 5 End Fraction , so the system is inconsistent.
1 answer