Answer
Option B is correct.
There is no solution. The lines are parallel.
Step-by-step explanation
When the equation of two lines are given, the solution is usually obtained from the point of intersection of the two lines.
But, it should be noted that, if the equations of the lines reduce to the same equation, then there won't be a solution for that system of equations.
Also, if the two lines are parallel to each other, they wont be able to ever intersect and would never have a solution too.
Two lines are said to be parallel when they have the same slopes.
The slope and y-intercept form of the equation of a straight line is given as
y = mx + c
where
y = y-coordinate of a point on the line.
m = slope of the line.
x = x-coordinate of the point on the line whose y-coordinate is y.
c = y-intercept of the line.
The two equations are
x - y = -1
-x + y = -1
The equations are not the same.
But we can find the slopes of each line and compare.
x - y = -1
-y = -x - 1
Multipl through by -1
y = x + 1
Comparing this to y = mx + c,
m = slope = 1
For the second equation,
-x + y = -1
y = x - 1
Comparing this to y = mx + c,
m = slope = 1
Since the slopes of the two lines are the same, the two lines can be said to be parallel to each other. Hence, they will never intersect and this system of equations will have no solutions.
Hope this Helps!!!