Answer
There is no solution between the 2 equations.
See Graph I for the graphing of the solution.
Work Step by Step
$x^2 + y^2 = 9 \longrightarrow (i)$
$x + y = 5 \longrightarrow (ii)$
From $(ii)$, we have
$x + y = 5$
$x = -y + 5 \longrightarrow (iii)$
Sub. $(iii)$ into $(i)$, we have
$(-y+5)^2 + y^2 = 9$
$y^2 - 10y + 25 + y^2 = 9$
$2y^2 - 10y + 16 = 0$
$y^2 - 5y + 8 = 0$
By means of quadratic formula, since Discriminant D = $(-5)^2$ - 4x1x8 = - 7 (less than 0), there will be no real roots with y, and therefore, there is no intersection between the 2 equations.
See Graph I for the graphing of the solution.
