Solve the system by the substitution or elimination method. $$\left( \begin{array} { r l }
x ^ { 2 } + y ^ { 2 } & = 44 \
x - y & = 10
\end{array} \right)$$
A) $( 5 + i \sqrt { 3 } , - 5 + i \sqrt { 3 } ) , ( 5 - i \sqrt { 3 } , - 5 - i \sqrt { 3 } )$
B) $( 5 - i \sqrt { 3 } , - 5 + i \sqrt { 3 } ) , ( 5 + i \sqrt { 3 } , - 5 - i \sqrt { 3 } )$
C) $( 5 + i \sqrt { 3 } , - 5 + i \sqrt { 3 } )$
D) $( 5 - i \sqrt { 3 } , - 5 - i \sqrt { 3 } )$

Question

Solve the system by the substitution or elimination method. $$\left( \begin{array} { r l } 
x ^ { 2 } + y ^ { 2 } & = 44 \
x - y & = 10
\end{array} \right)$$
A) $( 5 + i \sqrt { 3 } , - 5 + i \sqrt { 3 } ) , ( 5 - i \sqrt { 3 } , - 5 - i \sqrt { 3 } )$
B) $( 5 - i \sqrt { 3 } , - 5 + i \sqrt { 3 } ) , ( 5 + i \sqrt { 3 } , - 5 - i \sqrt { 3 } )$
C) $( 5 + i \sqrt { 3 } , - 5 + i \sqrt { 3 } )$
D) $( 5 - i \sqrt { 3 } , - 5 - i \sqrt { 3 } )$

Quizplus · Accepted Answer

From the second equation, $x = y + 10$. Substituting $x$ in the first equation, $(y + 10)^2 + y^2 = 44$, simplifying gives a quadratic equation in $y$, which when solved gives complex solutions for $y$, and subsequently for $x$. The correct complex solutions are given in option A.

Solve the System by the Substitution or Elimination Method (x2+y2=44x−y=10)\left( \begin{array} { r l } x ^ { 2 } + y ^ { 2 } & = 44 \\x - y & = 10\end{array} \right)(x2+y2x−y​=44=10​)

Solve the System by the Substitution or Elimination Method $\left( \begin{array} { r l } x ^ { 2 } + y ^ { 2 } & = 44 \\x - y & = 10\end{array} \right)$