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)
• 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 are parallel.
• The statement is false, because the lines are parallel.

Answer 1

The correct choice is: "The statement is true, because the lines are parallel."

Explanation: Rewriting x + y = 8 gives y = -x + 8. Both lines have slope -1 but different y‑intercepts (3 and 8), so they are distinct parallel lines and do not intersect, hence no solution.