Solve the nonlinear system of equations for real solutions.
-$\left\{ \begin{array} { l }
x ^ { 2 } + 2 y ^ { 2 } = - 7 \
x - y = - 9
\end{array} \right.$
A)
$\left( \frac { 9 + \sqrt { 345 } } { 3 } , \frac { - 18 + \sqrt { 345 } } { 3 } \right) , \left( \frac { 9 + \sqrt { 345 } } { 3 } , \frac { - 18 - \sqrt { 345 } } { 3 } \right) , \left( \frac { 9 - \sqrt { 345 } } { 3 } , \frac { - 18 + \sqrt { 345 } } { 3 } \right)$, $\left\{ \frac { 9 - \sqrt { 345 } } { 3 } , \frac { - 18 - \sqrt { 345 } } { 3 } \right\}$
B)
$\left\{ \frac { - 18 + \sqrt { 345 } } { 3 } , \frac { 9 + \sqrt { 345 } } { 3 } \right) , \left( \frac { - 18 + \sqrt { 345 } } { 3 } , \frac { 9 - \sqrt { 345 } } { 3 } \right) , \left( \frac { - 18 - \sqrt { 345 } } { 3 } , \frac { 9 + \sqrt { 345 } } { 3 } \right)$,
$- 18$ $\varnothing$
C) $\varnothing$
D) $( 0,0 )$

Question

Solve the nonlinear system of equations for real solutions.
-$\left\{ \begin{array} { l } 
x ^ { 2 } + 2 y ^ { 2 } = - 7 \
x - y = - 9
\end{array} \right.$
A)
$\left( \frac { 9 + \sqrt { 345 } } { 3 } , \frac { - 18 + \sqrt { 345 } } { 3 } \right) , \left( \frac { 9 + \sqrt { 345 } } { 3 } , \frac { - 18 - \sqrt { 345 } } { 3 } \right) , \left( \frac { 9 - \sqrt { 345 } } { 3 } , \frac { - 18 + \sqrt { 345 } } { 3 } \right)$, $\left\{ \frac { 9 - \sqrt { 345 } } { 3 } , \frac { - 18 - \sqrt { 345 } } { 3 } \right\}$
B)
$\left\{ \frac { - 18 + \sqrt { 345 } } { 3 } , \frac { 9 + \sqrt { 345 } } { 3 } \right) , \left( \frac { - 18 + \sqrt { 345 } } { 3 } , \frac { 9 - \sqrt { 345 } } { 3 } \right) , \left( \frac { - 18 - \sqrt { 345 } } { 3 } , \frac { 9 + \sqrt { 345 } } { 3 } \right)$,
$- 18$ $\varnothing$
C) $\varnothing$
 D) $( 0,0 )$

Quizplus · Accepted Answer

Given the equation $x^2 + 2y^2 = -7$, it's clear that for any real numbers $x$ and $y$, the left side will always be non-negative (since squares of real numbers are non-negative), while the right side is negative. This means there are no real solutions that satisfy this equation, making all other options incorrect.

Solve the Nonlinear System of Equations for Real Solutions {x2+2y2=−7x−y=−9\left\{ \begin{array} { l } x ^ { 2 } + 2 y ^ { 2 } = - 7 \\x - y = - 9\end{array} \right.{x2+2y2=−7x−y=−9​

Solve the Nonlinear System of Equations for Real Solutions $\left\{ \begin{array} { l } x ^ { 2 } + 2 y ^ { 2 } = - 7 \\x - y = - 9\end{array} \right.$