Give All Solutions of the Nonlinear System of Equations, Including $$\begin{array} { l } 5 x ^ { 2 } - 5 y ^ { 2 } = - 60 \\3 x ^ { 2 } + 4 y ^ { 2 } = 76\end{array}$$

question 327

Multiple Choice

Give all solutions of the nonlinear system of equations, including those with nonreal complex components.
- $$\begin{array} { l } 5 x ^ { 2 } - 5 y ^ { 2 } = - 60 \\3 x ^ { 2 } + 4 y ^ { 2 } = 76\end{array}$$

• A) \(\{ ( 2,4 ) , ( 4,2 ) , ( - 2 , - 4 ) , ( - 4 , - 2 ) \}\)
• B) \(\{ ( - 2 , - 4 ) , ( - 4 , - 2 ) \}\)
• C) \(\{ ( 2 , - 4 ) , ( 2,4 ) \}\)
• D) \(\{ ( 2,4 ) , ( - 2,4 ) , ( 2 , - 4 ) , ( - 2 , - 4 ) \}\)

---

Definitions:

Nucleus Accumbens

A region in the brain that plays a significant role in the reward circuit, associated with pleasure and reinforcement.

Brain Injury

Physical trauma to the brain, which can lead to temporary or permanent impairment of cognitive, physical, and psychosocial functions.

Meningitis

Meningitis is an inflammation of the protective membranes covering the brain and spinal cord, potentially leading to serious health complications or death, and can be caused by infections or other factors.

Traumatic Brain Injury

Damage to the brain resulting from external mechanical force, such as a blow, jolt, or penetrating injury to the head.