Sylvie finds the solution to the system of equations by graphing. y = x + 1 and y = x – 1 which graph shows the solution to sylvie’s system of equations?

Graphs of y = x+- 1 and of y = x - 1 are shown in the figure below.
The intersection of the two graphs is the solution for the two equations.

There is no solution.

Explanation:
It is clear that the two lines are parallel and will never intersect.

Note that the equation for a straight line is of the form
y = mx + b
where
m = slope,
b = y-intercept.

y = x + 1 has slope of m=1.
y = x - 1 has slope of m=1.
The two slopes are equal.
Because parallel lines do not intercept, there is no solution.