Solve: $\left\{ \begin{array} { l }
x ^ { 2 } + y ^ { 2 } = 36 \
x ^ { 2 } - y ^ { 2 } = 36
\end{array} \right.$
A) $\{ ( 6,0 ) \}$
B) $\{ ( 36,0 ) \}$
C) $\{ ( 6,0 ) , ( - 6,0 ) \} \}$
D) $\{ ( 0,6 ) , ( 0 , - 6 ) \}$

Question

Solve: $\left\{ \begin{array} { l } 
x ^ { 2 } + y ^ { 2 } = 36 \
x ^ { 2 } - y ^ { 2 } = 36
\end{array} \right.$
A) $\{ ( 6,0 ) \}$
B) $\{ ( 36,0 ) \}$
C) $\{ ( 6,0 ) , ( - 6,0 ) \} \}$
D) $\{ ( 0,6 ) , ( 0 , - 6 ) \}$

Quizplus · Accepted Answer

Adding the two equations, we get $2x^2 = 72$, which simplifies to $x^2 = 36$, giving $x = 6$ or $x = -6$. Substituting $x = 6$ or $x = -6$ into either equation shows $y = 0$. Therefore, the solutions are $\{(6,0), (-6,0)\}$.

Solve {x2+y2=36x2−y2=36\left\{ \begin{array} { l } x ^ { 2 } + y ^ { 2 } = 36 \\x ^ { 2 } - y ^ { 2 } = 36\end{array} \right.{x2+y2=36x2−y2=36​

Solve $\left\{ \begin{array} { l } x ^ { 2 } + y ^ { 2 } = 36 \\x ^ { 2 } - y ^ { 2 } = 36\end{array} \right.$