How many solutions does the following system have? y=x-2 -x+y=-5 no solutions infinitely many solutions two solutions one solution

To find how many solution our system has, we are going to find the slope of each equation.
equation (1)
equation (2)
To find the slope, we are going to express both equations in the form: 
where
is the slope

Notice that equation (1) is already in the form ; from equation (1) we can infer that 

To express equation (2) in the form , we are going to add  to both sides of the equation: 


Now, we can infer that the slope of equation (2) is . Since both equations have the same slope, we are dealing with parallel lines; parallel lines don't intercept, so the system has no solutions.

We can conclude that the correct answer is  the first choice: no solutions