Solve Nonlinear Systems By Addition
-$$\begin{array} { l }
x ^ { 2 } - y ^ { 2 } = 11 \
x ^ { 2 } + y ^ { 2 } = 25
\end{array}$$
A) $\{ ( 3 \sqrt { 2 } , \sqrt { 7 } ) , ( - 3 \sqrt { 2 } , \sqrt { 7 } ) , ( 3 \sqrt { 2 } , - \sqrt { 7 } ) , ( - 3 \sqrt { 2 } , - \sqrt { 7 } ) \}$
B) $\{ ( 0,0 ) \}$
C) $\{ ( 3 \sqrt { 2 } , \sqrt { 7 } ) , ( - 3 \sqrt { 2 } , - \sqrt { 7 } ) \}$
D) $\{ ( 3 \sqrt { 2 } , \sqrt { 7 } ) , ( - 3 \sqrt { 2 } , \sqrt { 7 } ) \}$

Question

Solve Nonlinear Systems By Addition
-$$\begin{array} { l } 
x ^ { 2 } - y ^ { 2 } = 11 \
x ^ { 2 } + y ^ { 2 } = 25
\end{array}$$
A) $\{ ( 3 \sqrt { 2 } , \sqrt { 7 } ) , ( - 3 \sqrt { 2 } , \sqrt { 7 } ) , ( 3 \sqrt { 2 } , - \sqrt { 7 } ) , ( - 3 \sqrt { 2 } , - \sqrt { 7 } ) \}$
B) $\{ ( 0,0 ) \}$
C) $\{ ( 3 \sqrt { 2 } , \sqrt { 7 } ) , ( - 3 \sqrt { 2 } , - \sqrt { 7 } ) \}$
D) $\{ ( 3 \sqrt { 2 } , \sqrt { 7 } ) , ( - 3 \sqrt { 2 } , \sqrt { 7 } ) \}$

Quizplus · Accepted Answer

Adding the two equations eliminates $y^2$, resulting in $2x^2 = 36$, which simplifies to $x^2 = 18$, giving $x = \pm 3\sqrt{2}$. Substituting $x$ back into one of the original equations allows solving for $y$, yielding $y = \pm \sqrt{7}$. Thus, all four combinations of $x$ and $y$ are solutions.

Solve Nonlinear Systems by Addition - x2−y2=11x2+y2=25\begin{array} { l } x ^ { 2 } - y ^ { 2 } = 11 \\x ^ { 2 } + y ^ { 2 } = 25\end{array}x2−y2=11x2+y2=25​

Solve Nonlinear Systems by Addition
- $\begin{array} { l } x ^ { 2 } - y ^ { 2 } = 11 \\x ^ { 2 } + y ^ { 2 } = 25\end{array}$