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To analyze the system of equations:
1. \( y = -x + 3 \)
2. \( x + y = 8 \)
We can rewrite the second equation in slope-intercept form (y = mx + b):
Starting from \( x + y = 8 \):
- Subtract \( x \) from both sides:
\[ y = -x + 8 \]
Now we can compare the two equations:
1. \( y = -x + 3 \) (slope = -1, y-intercept = 3)
2. \( y = -x + 8 \) (slope = -1, y-intercept = 8)
Since both lines have the same slope (-1) but different y-intercepts, they are parallel lines. Parallel lines will never intersect, which means there is no solution to the system of equations.
Thus, the statement is **true**, and the correct response is:
"The statement is true, because the lines are parallel."