Consider the system of equations.

Question

   y = –x + 3   y = –x – 3

The graph of the first equation is shown by the orange line.

On a coordinate plane, an orange line goes through points (0, 3) and (3, 0).

What is the slope of the orange line?
If the second equation was drawn on the same graph, what would be its slope?
If the lines of both equations were shown on the same graph, they would
.
The system of equations has
.

Answer 1

To solve your questions based on the system of equations given:

1. For the first equation, \( y = -x + 3 \):

   • The slope (m) is the coefficient of \( x \), which is \( -1 \).
   • Therefore, the slope of the orange line is -1.

2. For the second equation, \( y = -x - 3 \):

   • The slope is also the coefficient of \( x \), which again is \( -1 \).
   • Thus, the slope of the second line would also be -1.

3. Since both equations have the same slope (-1), the lines are parallel and will never intersect.

   • Therefore, if the lines of both equations were shown on the same graph, they would be parallel.

4. Since the two lines are parallel, they do not intersect at any point.

   • Hence, the system of equations has no solution.

In summary:

• The slope of the orange line is -1.
• The slope of the second line is also -1.
• The lines would be parallel.
• The system of equations has no solution.