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 have an intersection point.
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 are parallel.
The correct response is: The statement is false, because the lines have an intersection point.
When two lines do not intersect and are not parallel, they are said to be inconsistent and the system of equations has no solution. In this case, the lines y = -x + 3 and x + y = 8 intersect at the point (2, 6), showing that there is in fact a solution to the system.