Question
Use the image to answer the question.
A coordinate plane with 4 quadrants ranges from negative 10 to 10 in unit increments on both the x and y axes. A solid line and a dashed line with arrows at both the ends are drawn parallel to each other on the graph. The equation of the solid line is y equals negative x plus 3. The equation of the dashed line is x plus y equals 8.
Solving the system y=−x+3
and x+y=8
by graphing shows that there is no solution to the system. Is this statement true or false? Explain.
(1 point)
Responses
The statement is true, because the lines are parallel.
The statement is true, because the lines are parallel.
The statement is false, because the lines have an intersection point.
The statement is false, because the lines have an intersection point.
The statement is true, because the lines have an intersection point.
The statement is true, because the lines have an intersection point.
The statement is false, because the lines are parallel.
A coordinate plane with 4 quadrants ranges from negative 10 to 10 in unit increments on both the x and y axes. A solid line and a dashed line with arrows at both the ends are drawn parallel to each other on the graph. The equation of the solid line is y equals negative x plus 3. The equation of the dashed line is x plus y equals 8.
Solving the system y=−x+3
and x+y=8
by graphing shows that there is no solution to the system. Is this statement true or false? Explain.
(1 point)
Responses
The statement is true, because the lines are parallel.
The statement is true, because the lines are parallel.
The statement is false, because the lines have an intersection point.
The statement is false, because the lines have an intersection point.
The statement is true, because the lines have an intersection point.
The statement is true, because the lines have an intersection point.
The statement is false, because the lines are parallel.
Answers
Answered by
GPT-4o mini
The statement is true, because the lines are parallel.
This is supported by the fact that the solid line has the equation \( y = -x + 3 \), and the dashed line has the equation \( x + y = 8 \), which can be rearranged to \( y = -x + 8 \).
Both lines have the same slope of -1, indicating that they are parallel. Since parallel lines never intersect, there is no solution to the system of equations.
This is supported by the fact that the solid line has the equation \( y = -x + 3 \), and the dashed line has the equation \( x + y = 8 \), which can be rearranged to \( y = -x + 8 \).
Both lines have the same slope of -1, indicating that they are parallel. Since parallel lines never intersect, there is no solution to the system of equations.
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