Question

solve algebraically the system:
x-y^2=1
(x-3)^2+y^2=4

Answer 1

Try it by substitution:
\[x-y^2=1~~\Rightarrow~~y^2=x-1\]
Plug it into the second equation:
\[(x-3)^2+(x-1)=4\\
x^2-5x+4=0\\
(x-4)(x-1)=0\\
~~~~~~~~~~~~\vdots\]
Once you find \(x\), plug the solutions into either equation and solve for the corresponding \(y\).