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:

Government Transfer Expenditure

Government spending on programs that provide benefits to individuals or families without requiring direct payment or labor in return, such as social security or unemployment benefits.

Social Security Program

A government program designed to provide financial support to individuals during retirement, disability, or other conditions that affect income.

Progressive Income Tax

A taxing mechanism in which the tax rate increases as the taxable amount of income increases, taxing higher incomes at higher rates.

Average Tax Rate

The ratio of the total amount of taxes paid to the total tax base (taxable income or spending), expressed as a percentage.