Question

How many solutions does the following system have? y=x-2 -x+y=-5

Answer 1

To find how many solution our system has, we are going to find the slope of each equation.
$y=x-2$ equation (1)
$-x+y=-5$ equation (2)
To find the slope, we are going to express both equations in the form: $y=mx+b$
where
$m$ is the slope

Notice that equation (1) is already in the form $y=mx+b$; from equation (1) we can infer that $m=1$

To express equation (2) in the form $y=mx+b$, we are going to add $x$ to both sides of the equation: 
$-x+x+y=x-5$
$y=x+5$
Now, we can infer that the slope of equation (2) is $m=1$. 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