The correct response is:
The slope of both lines is 5, so the system is inconsistent.
Determine if the system is inconsistent by graphing and finding the slopes. x−5y=10 −3x+15y=30 (1 point) Responses 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. 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. 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. 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.
1 answer
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