Does the graph show the system of equations x+y=2

Question

x
+
y
=
2
and −x+y=7
−
x
+
y
=
7
? Should the lines for the system be parallel?

(1 point)
Responses

The graph of −x+y=7
−
x
+
y
=
7
is incorrect. The lines should intersect.
The graph of negative x plus y equals 7 is incorrect. The lines should intersect.

Both graphs are correct. The lines should be parallel.
Both graphs are correct. The lines should be parallel.

The graph of x+y=2
x
+
y
=
2
is incorrect. The lines should intersect.
The graph of x plus y equals 2 is incorrect. The lines should intersect.

The graph of −x+y=7
−
x
+
y
=
7
is incorrect. The lines should be parallel.

Answer 1

To determine whether the lines represented by the equations \( x + y = 2 \) and \( -x + y = 7 \) are parallel, let's analyze the equations.

1. The equation \( x + y = 2 \) can be rearranged to find its slope:

   • \( y = -x + 2 \)
   • The slope is \(-1\).

2. The equation \( -x + y = 7 \) can also be rearranged:

   • \( y = x + 7 \)
   • The slope is \(1\).

Since the slopes of the two lines are different (-1 for \( x + y = 2 \) and 1 for \( -x + y = 7 \)), the lines are not parallel; they will intersect at some point.

Thus, the correct response is: The graph of \( -x+y=7 \) is incorrect. The lines should intersect.