Question

What is the greatest possible number of solutions to the following system of equations

Answer 1

The answer to this question is 2
this is because it is the highest before it starts to turn into fractions and square roots.

I hope this helps!!!!!

Answer 2

Answer:

The greatest possible number of solutions is 2.

Step-by-step explanation:

Given system of equations,

$x^2+y^2=9-----(1)$

$9x+2y=16$

$9x=16-2y$

$\implies x=\frac{16-2y}{9}-----(2)$

From equation (1),

$(\frac{16-2y}{9})^2+y^2=9$

$\frac{(16-2y)^2}{81}+y^2=9$

$\frac{256-64y+4y^2}{81}+y^2=9$

$\frac{256-64y+4y^2+81y^2}{81}=9$

$85y^2-64y+256=729$

$85y^2-64y-473=0$

By quadratic formula we get,

$\implies y = \frac{32+9\sqrt{509}}{85}\text{ or }y=\frac{32-9\sqrt{509}}{85}$

By substituting these values in equation (2),

We get,

$x=\frac{144+2\sqrt{509}}{85}\text{ or }x=\frac{144-2\sqrt{509}}{85}$

Hence, all possible solutions of the given system of equations are,

$(\frac{144+2\sqrt{509}}{85},\frac{32+9\sqrt{509}}{85})\text{ and }(\frac{144-2\sqrt{509}}{85},\frac{32-9\sqrt{509}}{85})$

Option second is correct.