# Thread: Solving a system graphically and numerically

1. ## Solving a system graphically and numerically

Okay so I'm having trouble with a system involving a circle and a parabola. My book tells me to solve the system graphically and support my answer numerically. I don't know how to do this and really appreciate the help!!!

$\displaystyle x^2 + y^2 = 9$
$\displaystyle y=2-x^2$

2. Originally Posted by LoveBeachForever
Okay so I'm having trouble with a system involving a circle and a parabola. My book tells me to solve the system graphically and support my answer numerically. I don't know how to do this and really appreciate the help!!!

$\displaystyle x^2 + y^2 = 9$
$\displaystyle y=2-x^2$
$\displaystyle x^2 = 9 - y^2$
$\displaystyle y=2-(9 - y^2)=-7 + y^2$

Second equation gives $\displaystyle y^2 - y - 7 = 0$ which is a second degree equation

3. Okay so if $\displaystyle 0=y^2-y-7$

then I can use the quadratic and get $\displaystyle y=\frac{1 \pm \sqrt 29}{2}$

which is $\displaystyle y=3.193$ or $\displaystyle -2.193$
using that and plugging it back in i get:
$\displaystyle 3.193=2-x^2$
$\displaystyle x^2=1.193$
$\displaystyle x=1.092$ so the solution is at (3.193,1.092) correct?

then for the other one,
$\displaystyle -2.193=2-x^2$
but $\displaystyle x^2=-4.193$ which leaves me with an imaginary number. So I'm assuming that it means that just the other one is the solution. Am I right?

4. Originally Posted by LoveBeachForever
Okay so if $\displaystyle 0=y^2-y-7$

then I can use the quadratic and get $\displaystyle y=\frac{1 \pm \sqrt 29}{2}$

which is $\displaystyle y=3.193$ or $\displaystyle -2.193$
using that and plugging it back in i get:
$\displaystyle 3.193=2-x^2$
$\displaystyle x^2=1.193$
$\displaystyle x=1.092$ so the solution is at (3.193,1.092) correct?

then for the other one,
$\displaystyle -2.193=2-x^2$
but $\displaystyle x^2=-4.193$ which leaves me with an imaginary number. So I'm assuming that it means that just the other one is the solution. Am I right?
No
$\displaystyle 3.193=2-x^2$
$\displaystyle x^2=-1.193$=> no solution
$\displaystyle -2.193=2-x^2$
but $\displaystyle x^2=4.193$ => 2 solutions : sqrt(4.193) and -sqrt(4.193)