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 are parallel.
• 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.

Answer 1

To determine whether the statement is true or false, we need to analyze the two equations:

1. \( y = -x + 3 \) is in slope-intercept form, where the slope is \(-1\) and the y-intercept is \(3\).
2. The second equation, \( x + y = 8 \), can be rewritten in slope-intercept form as \( y = -x + 8 \). Here, the slope is also \(-1\), and the y-intercept is \(8\).

Since both lines have the same slope of \(-1\) but different y-intercepts (\(3\) and \(8\)), they are parallel. Parallel lines do not intersect, which means they have no solutions in terms of points of intersection.

Thus, the statement is true: there is no solution to the system because the lines are parallel.

The correct explanation from the provided options is:

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