Solve the system of nonlinear equations by the addition method. $$9 x ^ { 2 } + 8 x y = 64$$
$$x ^ { 2 } - x y = 9$$
A) $\left\{ \left( - \sqrt { 8 } , \frac { \sqrt { 8 } } { 8 } \right) , \left( \sqrt { 8 } , - \frac { \sqrt { 8 } } { 8 } \right) \right\}$
B) $\left\{ \left( - \sqrt { 8 } , - \frac { \sqrt { 8 } } { 8 } \right) , \left( \sqrt { 8 } , \frac { \sqrt { 8 } } { 8 } \right) \right\}$
C) $\left\{ \left( - \sqrt { 8 } , \frac { \sqrt { 8 } } { 8 } \right) , \left( \sqrt { 8 } , \frac { \sqrt { 8 } } { 8 } \right) \right\}$
D){ }

Question

Quizplus · Accepted Answer

Multiply the second equation by 8 to get $8 x ^ { 2 } - 8 x y = 72$. Add this to the first equation to get $17 x ^ { 2 } = 136$, so $x ^ { 2 } = 8$ and $x = \pm \sqrt { 8 } $. Substituting these values of $x$ into the second equation gives $y = \pm \frac { \sqrt { 8 } } { 8 }$. So the solutions are $\left( - \sqrt { 8 } , \frac { \sqrt { 8 } } { 8 } \right)$ and $\left( \sqrt { 8 } , - \frac { \sqrt { 8 } } { 8 } \right)$.

Solve the System of Nonlinear Equations by the Addition Method 9x2+8xy=649 x ^ { 2 } + 8 x y = 649x2+8xy=64

Solve the System of Nonlinear Equations by the Addition Method $9 x ^ { 2 } + 8 x y = 64$