**Re: Points of intersection**
Hello, AGlas9837!
Find the points of intersection, if any, of the graphs of the equations:

. . \(\displaystyle x^2+y^2 \:=\:25\,\text{ and }\,2x+y\:=\:10\)

\(\displaystyle \text{You made a }really\text{ silly mistake . . .}\)

\(\displaystyle x^2+y^2 \:=\:25 \quad\Rightarrow\quad y^2 \:=\:25 - x^2 \quad\Rightarrow\quad y \:=\:\om\sqrt{25-x^2}\)

. . \(\displaystyle \text{Then you took the square root ??}\)

\(\displaystyle \text{"Substitution" is the method to use.}\)

\(\displaystyle \text{The second equation gives us: }\:y \:=\:10-2x\)

\(\displaystyle \text{Substitute into the first: }\;x^2 + (10-2x)^2 \:=\:25\)

. . \(\displaystyle \text{which simplifies to: }\:x^2-8x+15 \:=\:0\)

\(\displaystyle \text{Got it?}\)