Solve Nonlinear Systems By Addition
Solve the system by the addition method.
-$$\begin{array} { l }
x ^ { 2 } - 3 y ^ { 2 } = 1 \
2 x ^ { 2 } + 3 y ^ { 2 } = 74
\end{array}$$
A) $\{ ( 5,8 ) , ( - 5,8 ) , ( 5 , - 8 ) , ( - 5 , - 8 ) \}$
B) $\{ ( 5,8 ) , ( - 5 , - 8 ) \}$
C) $\{ ( 8,5 ) , ( - 8,5 ) , ( 8 , - 5 ) , ( - 8 , - 5 ) \}$
D) $\{ ( 8,5 ) , ( - 8 , - 5 ) \}$

Question

Solve Nonlinear Systems By Addition
Solve the system by the addition method.
-$$\begin{array} { l } 
x ^ { 2 } - 3 y ^ { 2 } = 1 \
2 x ^ { 2 } + 3 y ^ { 2 } = 74
\end{array}$$
A) $\{ ( 5,8 ) , ( - 5,8 ) , ( 5 , - 8 ) , ( - 5 , - 8 ) \}$
B) $\{ ( 5,8 ) , ( - 5 , - 8 ) \}$
C) $\{ ( 8,5 ) , ( - 8,5 ) , ( 8 , - 5 ) , ( - 8 , - 5 ) \}$
D) $\{ ( 8,5 ) , ( - 8 , - 5 ) \}$

Quizplus · Accepted Answer

By adding the equations, we eliminate $y^2$ and solve for $x^2$, then substitute back to find $y$. The solutions are $(5,8), (-5,8), (5,-8), (-5,-8)$.

Solve Nonlinear Systems by Addition Solve the System by the Addition

Solve Nonlinear Systems by Addition
Solve the System by the Addition