Give all solutions of the nonlinear system of equations, including those with nonreal complex components.
$\begin{array} { l }
x y = 1 \
28 x - y = 3
\end{array}$
A) $\left\{ \left( - \frac { 1 } { 7 } , - 7 \right) , \left( \frac { 1 } { 4 } , 4 \right) \right\}$
B) $\left\{ \left( \frac { 1 } { 4 } , 4 \right) \right\}$
C) $\{ ( 7 , - 7 ) , ( - 4,4 ) \}$
D) $\left\{ \left( - 7 , - \frac { 1 } { 7 } \right) , \left( 4 , \frac { 1 } { 4 } \right) \right\}$

Question

Give all solutions of the nonlinear system of equations, including those with nonreal complex components.
$\begin{array} { l } 
x y = 1 \
28 x - y = 3
\end{array}$
A) $\left\{ \left( - \frac { 1 } { 7 } , - 7 \right) , \left( \frac { 1 } { 4 } , 4 \right) \right\}$
B) $\left\{ \left( \frac { 1 } { 4 } , 4 \right) \right\}$
C) $\{ ( 7 , - 7 ) , ( - 4,4 ) \}$
D) $\left\{ \left( - 7 , - \frac { 1 } { 7 } \right) , \left( 4 , \frac { 1 } { 4 } \right) \right\}$

Quizplus · Accepted Answer

To solve the system, substitute $y = \frac{1}{x}$ from the first equation into the second equation to get $28x - \frac{1}{x} = 3$. Multiplying through by $x$ gives a quadratic equation $28x^2 - 3x - 1 = 0$. Solving this quadratic equation gives the x-values, and substituting these back into $y = \frac{1}{x}$ gives the corresponding y-values, which match the solutions in option A.

Give All Solutions of the Nonlinear System of Equations, Including xy=128x−y=3\begin{array} { l } x y = 1 \\28 x - y = 3\end{array}xy=128x−y=3​

Give All Solutions of the Nonlinear System of Equations, Including $\begin{array} { l } x y = 1 \\28 x - y = 3\end{array}$