Solve the system of equations algebraically for real values of x and y. $$\left\{ \begin{array} { l }
x ^ { 2 } + y ^ { 2 } = 41 \
y = x ^ { 2 } - 11
\end{array} \right.$$
A) $\quad ( 4,5 ) , ( - 4,5 )$
B) $\quad ( 5,4 ) , ( - 4,5 )$
C) $\quad ( 4,5 ) , ( 5 , - 4 )$
D) $\quad ( - 4,5 ) , ( 4,9 )$
E) $\quad ( 9,5 ) , ( 5 , - 4 )$

Question

Solve the system of equations algebraically for real values of x and y. $$\left\{ \begin{array} { l } 
x ^ { 2 } + y ^ { 2 } = 41 \
y = x ^ { 2 } - 11
\end{array} \right.$$
A) $\quad ( 4,5 ) , ( - 4,5 )$
B) $\quad ( 5,4 ) , ( - 4,5 )$
C) $\quad ( 4,5 ) , ( 5 , - 4 )$
D) $\quad ( - 4,5 ) , ( 4,9 )$
E) $\quad ( 9,5 ) , ( 5 , - 4 )$

Quizplus · Accepted Answer

Substitute $y = x^2 - 11$ into the first equation to get $x^2 + (x^2 - 11)^2 = 41$. Solve for $x$ and then find $y$ using the second equation. The solutions are $(4,5)$ and $(-4,5)$.

Solve the System of Equations Algebraically for Real Values of X