To analyze the system of equations:
- \( y = -r + 3 \) (This is a linear equation in terms of r and y, representing a line in the y-r plane.)
- \( z + y = 8 \) can be rewritten as \( y = 8 - z \) (This represents another line in the y-z plane).
Now let's consider the given situation:
- The first equation describes a line in a vertical plane where y can take different values as r varies.
- The second equation is a line in the y-z plane where y can take different values as z varies.
Since the expressions involve different variables (r in the first equation, and z in the second), they define planes rather than lines. Therefore, there is no intersection point or parallel line situation directly between these two equations in a typical sense.
Since the first equation is defined in terms of \( r \) and \( y \), and the second one in terms of \( z \) and \( y \), it leads to a misunderstanding when framing it as just two lines intersecting.
In conclusion, because these are equations defining planes with different variable relationships rather than linear equations in the same variable set, it is not correct to categorize the system as having no solution based on graphing them.
Hence, the correct statement is:
- The statement is false, because the lines have an intersection point.
However, the logical interpretation regarding intersection points doesn't apply as-is because of varying dimensions in the variables. A review shows we are not truly dealing with two 2D lines but effectively understanding intersection in a higher spatial dimension. Thus, clearer context is required for consistent interpretative accuracy.