How many solutions does the following system have? y=x-2 -x+y=-5
1 answer:
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: <span>no solutions</span>
To find the slope, we are going to express both equations in the form:
where
Notice that equation (1) is already in the form
To express equation (2) in the form
Now, we can infer that the slope of equation (2) is
We can conclude that the correct answer is the first choice: <span>no solutions</span>
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