Question

Use the image to answer the question.
x + y = 8
y = -x + 3
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.
A. The statement is true, because the lines are parallel.
B. The statement is false, because the line have an intersection point.
C. The statement is false, because the lines are parallel.
D. The statement is true, because the lines have an intersection point.

Answer 1

To determine the truth of the statement, we need to analyze the system of equations given:

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

We can rewrite the first equation in slope-intercept form \( y = mx + b \):

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

Now we can compare the two equations:

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

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.