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 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 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 have an intersection point.

Answer 1

To analyze the given system:

1. The first equation is \( y = -x + 3 \).
2. The second equation can be rewritten in slope-intercept form as follows:
\[
x + y = 8 \implies y = -x + 8.
\]

Now, we can observe the slopes and y-intercepts of both lines:

- The first line \( y = -x + 3 \) has a slope of -1 and a y-intercept of 3.
- The second line \( y = -x + 8 \) also has a slope of -1 but a y-intercept of 8.

Since both lines have the same slope (-1), they are parallel. Parallel lines do not intersect, which means there is no solution to the system of equations, as they will never meet.

Based on this analysis, the correct statement is:

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