One Solution, No Solution, or Many Solutions Quick Check 2 of 52 of 5 Items Question Use the image to answer the question. 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 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. The statement is false, because the lines are parallel. The statement is false, because the lines have an intersection point.
The statement is true, because the lines are parallel. This can be determined by looking at the slopes of the two equations. The first equation is in the form y=-x+3, which has a slope of -1. The second equation is in the form x+y=8, which can be rearranged to y=-x+8, with a slope of -1. Since the slopes are the same, the lines are parallel and there is no intersection point, meaning there is no solution to the system.
