Solve the following using substitution x2 + y2 = 13 y = x2 - 1 there are two solutions with x and y as ordered pairs i've been trying to this for an hour. the 2 after x and y is squared/ an exponent.

Hello! We have a system of equations here, so there are a few ways to solve it, but I'll use the substitution method. We have



The second equation gives us y in terms of x, so we'll plug that into the first equation and solve:







Now we have the tricky part. Initially, you may think that there are three x values that are relevant, but in reality we can never make the term equal to 0 because can only go as small as zero itself. This means we only care about the other two factors, so:
and . Then and .

Now we need to find out which y-values correspond to these x-values. I'll use the second equation to do this:



So our points are (-2,3) and (2,3).