Y=X^2-2x+3
Y=x+1

Solve by using substitution or elimination

You can set the equations equal to each other since they both equal Y, and then solve for x.
Or set the bottom equation equal to X (so x=y-1) and then substitute that for the x in the first equation.

Example:

Y=(Y-1)^2 - 2(Y-1) + 3
Y=(Y^2 -1Y -1Y + 1) - 2Y + 2 + 3
Y= Y^2 -2Y +1 -2Y +5
Y= Y^2 -4Y +6
0= Y^2 -5Y +6

And then factor:

0= Y^2 -3Y -2Y +6
0= Y(Y-3) + -2(Y-3)
0= (Y-2) (Y-3)
Y= 2 or 3

And then take those numbers and plug them into the bottom equation and solve for X. You should get something like (2,3) and (1,2) as answers.

This should be the way to do it. I might have made a multiplication or addition mistake on the way but the process should be the same. Please double check my work and let me know if I did indeed make a mistake.
Thank you, hope this helps :)