Solving the system y=−x+3

Question

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 false, because the lines have an intersection point.
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 have an intersection point.

The statement is true, because the lines are parallel.

Answer 1

To analyze the given system of equations:

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

First, we'll rewrite the second equation in slope-intercept form (y = mx + b):

• Starting with \( x + y = 8 \), we can isolate \( y \): \[ y = -x + 8 \]

Now we have two equations:

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

Both lines have the same slope of -1, which means they are parallel. Since parallel lines never intersect, the system of equations has no solution.

Thus, the statement "Solving the system by graphing shows that there is no solution to the system" is true.

The correct response is:

The statement is true, because the lines are parallel.