To determine the truth of the statement, we need to analyze the system of equations given:
- \( x + y = 8 \)
- \( y = -x + 3 \)
We can rewrite the first equation in slope-intercept form \( y = mx + b \):
- \( y = -x + 8 \)
Now we can compare the two equations:
- \( y = -x + 8 \)
- \( y = -x + 3 \)
Both equations have the same slope of -1, indicating that the lines are indeed parallel. Since these lines are parallel, they will never intersect, which means there is no solution to the system.
The correct answer is:
A. The statement is true, because the lines are parallel.