Question

Use the image to answer the question.



Solving the system y=−x+3
𝑦
=
−
𝑥
+
3
and x+y=8
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 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 p

Answer 1

The statement is **false**.

To explain, when solving a system of equations by graphing, if the lines representing the equations intersect at a point, it means there is a solution to the system (the coordinates of the intersection point). In the provided equations:

1. \( y = -x + 3 \) is a line with a negative slope that crosses the y-axis at 3.
2. \( x + y = 8 \) can be rewritten as \( y = -x + 8 \), which is also a line with a negative slope that crosses the y-axis at 8.

When graphed, these two lines are parallel (since they have the same slope of -1) and will never intersect, indicating there is no solution to the system of equations. Therefore, the corrected understanding is that the statement is false because the lines do not intersect, confirming that there is no solution.