Solve Nonlinear Systems By Addition
-$$\begin{array} { l }
x ^ { 2 } - y ^ { 2 } = 25 \
4 x ^ { 2 } + 25 y ^ { 2 } = 100
\end{array}$$
A) $\{ ( 5,0 ) , ( - 5,0 ) \}$
B) $\{ ( 2,0 ) , ( - 2,0 ) \}$
C) $\{ ( 0,5 ) , ( 0 , - 5 ) \}$
D) $\{ ( 0,2 ) , ( 0 , - 2 ) \}$

Question

Solve Nonlinear Systems By Addition
-$$\begin{array} { l } 
x ^ { 2 } - y ^ { 2 } = 25 \
4 x ^ { 2 } + 25 y ^ { 2 } = 100
\end{array}$$
A) $\{ ( 5,0 ) , ( - 5,0 ) \}$
B) $\{ ( 2,0 ) , ( - 2,0 ) \}$
C) $\{ ( 0,5 ) , ( 0 , - 5 ) \}$
D) $\{ ( 0,2 ) , ( 0 , - 2 ) \}$

Quizplus · Accepted Answer

To solve the system, we can add the two equations together to eliminate $y^2$. The first equation is $x^2 - y^2 = 25$, and the second equation is $4x^2 + 25y^2 = 100$. Adding these equations gives $5x^2 = 125$, which simplifies to $x^2 = 25$. Solving for $x$ gives $x = 5$ or $x = -5$. Substituting $x = 5$ and $x = -5$ back into one of the original equations shows that $y = 0$. Therefore, the solutions are $(5,0)$ and $(-5,0)$.

Solve Nonlinear Systems by Addition - x2−y2=254x2+25y2=100\begin{array} { l } x ^ { 2 } - y ^ { 2 } = 25 \\4 x ^ { 2 } + 25 y ^ { 2 } = 100\end{array}x2−y2=254x2+25y2=100​

Solve Nonlinear Systems by Addition
- $\begin{array} { l } x ^ { 2 } - y ^ { 2 } = 25 \\4 x ^ { 2 } + 25 y ^ { 2 } = 100\end{array}$