Question

solve the non-linear system of equations for real solution...

Answer 1

\[x^2 + 5y^2 =2\]
\[x^2 - 5y^2 =14\]

Answer 2

im thinking the answer is no solution

Answer 3

but im not sure

Answer 4

Hmm..

Answer 5

cause when i solve for y in the first equation im getting sqroot -12/10

Answer 6

Well, the first is an elipse, so you are looking for intersections between an ellipse and a hyperbola.

Answer 7

ya

Answer 8

im using the substitution method

Answer 9

Treating it as a matrix.

Answer 10

i haven't gotten into matrices yet...

Answer 11

If you add the two equations you will see that:\[2x^2=16\Longrightarrow x^2=8.\]But if you substitute that back into either of the two equations, you get:\[x^2+5y^2=2\Longrightarrow 8+5y^2=2\Longrightarrow 5y^2=-6\]which has no real solutions. So you are correct in saying there are no real solutions.

Answer 12

k, thx!

Answer 13

give a medal to mcc also

Answer 14

Visually it is this:

https://www.desmos.com/calculator/lhva6f9mdv

Answer 15

So good question and you were thinking correclty about it.