We can check our answers by substituting the points into both equations. If they produce true statements, our solutions are correct. Let's start by checking
(-2,2). We will substitute
-2 and
2 for
x and
y, respectively, in Equation (I) and Equation (II).
{x2+y2=8x+y=0
{(-2)2+22=?8-2+2=?0
{8=8 ✓0=0 ✓
Since both equations produced true statements, the solution
(-2,2) is correct. Let's now check
(2,-2).
{x2+y2=8x+y=0
{22+(-2)2=?82+(-2)=?0
{4+4=?82+(-2)=?0
{4+4=?82−2=?0
(I), (II): Add and subtract terms
{8=8 ✓0=0 ✓
Since again both equations produce true statements, the solution
(2,-2) is also correct.