Solve Nonlinear Systems By Addition
Solve the system by the addition method.
-$$\begin{array} { l }
x ^ { 2 } - y ^ { 2 } = 9 \
x ^ { 2 } + y ^ { 2 } = 51
\end{array}$$
A) $\{ ( \sqrt { 30 } , \sqrt { 21 } ) , ( - \sqrt { 30 } , \sqrt { 21 } ) , ( \sqrt { 30 } , - \sqrt { 21 } ) , ( - \sqrt { 30 } , - \sqrt { 21 } ) \}$
B) $\{ ( 0,0 ) \}$
C) $\{ ( \sqrt { 30 } , \sqrt { 21 } ) , ( - \sqrt { 30 } , - \sqrt { 21 } ) \}$
D) $\{ ( \sqrt { 30 } , \sqrt { 21 } ) , ( - \sqrt { 30 } , \sqrt { 21 } ) \}$

Question

Solve Nonlinear Systems By Addition
Solve the system by the addition method.
-$$\begin{array} { l } 
x ^ { 2 } - y ^ { 2 } = 9 \
x ^ { 2 } + y ^ { 2 } = 51
\end{array}$$
A) $\{ ( \sqrt { 30 } , \sqrt { 21 } ) , ( - \sqrt { 30 } , \sqrt { 21 } ) , ( \sqrt { 30 } , - \sqrt { 21 } ) , ( - \sqrt { 30 } , - \sqrt { 21 } ) \}$
B) $\{ ( 0,0 ) \}$
C) $\{ ( \sqrt { 30 } , \sqrt { 21 } ) , ( - \sqrt { 30 } , - \sqrt { 21 } ) \}$
D) $\{ ( \sqrt { 30 } , \sqrt { 21 } ) , ( - \sqrt { 30 } , \sqrt { 21 } ) \}$

Quizplus · Accepted Answer

Adding the two equations eliminates $y^2$, resulting in $2x^2 = 60$, which simplifies to $x^2 = 30$. Thus, $x = \pm\sqrt{30}$. Substituting $x^2 = 30$ into either equation allows solving for $y^2$, leading to $y^2 = 21$ and $y = \pm\sqrt{21}$. This results in four combinations of $x$ and $y$.

Solve Nonlinear Systems by Addition Solve the System by the Addition

Solve Nonlinear Systems by Addition
Solve the System by the Addition