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 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 false, because the lines have an intersection point. The statement is true, because the lines are parallel.

Answer 1

To determine the validity of the statement, we need to analyze the two equations given:

1. \( y = -x + 3 \)
2. \( x + y = 8 \)

We can rewrite the second equation in slope-intercept form (i.e., \( y = mx + b \)):

Starting with \( x + y = 8 \):

\[
y = -x + 8
\]

Now we have both equations in slope-intercept form:

1. \( y = -x + 3 \)
2. \( y = -x + 8 \)

Next, we can see that both equations have the same slope (\(-1\)), which means they are parallel lines. Since parallel lines never intersect, there is no solution to the system.

Based on this analysis, the correct response to the statement is:

**The statement is true, because the lines are parallel.**