Solve the system of equations using elimination.
-$$\left\{ \begin{array} { l }
x ^ { 2 } + y ^ { 2 } = 61 \
x ^ { 2 } - y ^ { 2 } = 11
\end{array} \right.$$
A) x = -6, y = -5; x = -5, y = -6
B) x = 6, y = 5; x = -6, y = 5; x = 6, y = -5; x = -6, y = -5
C) x = 6, y = -5; x = 6, y = 5
D) x = 6, y = 5; x = 5, y = 6; x = -6, y = -5; x = -5, y = -6

Question

Solve the system of equations using elimination.
-$$\left\{ \begin{array} { l } 
x ^ { 2 } + y ^ { 2 } = 61 \
x ^ { 2 } - y ^ { 2 } = 11
\end{array} \right.$$
A) x = -6, y = -5; x = -5, y = -6
B) x = 6, y = 5; x = -6, y = 5; x = 6, y = -5; x = -6, y = -5
C) x = 6, y = -5; x = 6, y = 5
D) x = 6, y = 5; x = 5, y = 6; x = -6, y = -5; x = -5, y = -6

Quizplus · Accepted Answer

Adding the two equations, we get $2x^2 = 72$, so $x^2 = 36$, giving $x = \pm6$. Subtracting the second equation from the first gives $2y^2 = 50$, so $y^2 = 25$, giving $y = \pm5$. Thus, all combinations of $x = \pm6$ and $y = \pm5$ are solutions.

Solve the System of Equations Using Elimination {x2+y2=61x2−y2=11\left\{ \begin{array} { l } x ^ { 2 } + y ^ { 2 } = 61 \\x ^ { 2 } - y ^ { 2 } = 11\end{array} \right.{x2+y2=61x2−y2=11​

Solve the System of Equations Using Elimination $\left\{ \begin{array} { l } x ^ { 2 } + y ^ { 2 } = 61 \\x ^ { 2 } - y ^ { 2 } = 11\end{array} \right.$