Question

Solving the system y=−x+3
𝑦
=
−
𝑥
+
3
and x+y=8
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 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 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.

Answer 1

True — the lines are parallel.

y = −x + 3 and x + y = 8 => y = −x + 8. Both have slope −1 but different y‑intercepts (3 and 8), so they never intersect. Substituting y = −x + 3 into x + y = 8 gives 3 = 8, a contradiction, confirming no solution.