Determine if each ordered pair is a solution to the given system of inequalities in two variables.
-$$\begin{array} { l }
x y = 54 \
x ^ { 2 } + y ^ { 2 } = 117
\end{array}$$
(i) $( 6 , - 9 )$; (ii) $( - 9 , - 6 )$
A) (i) Yes; (ii) Yes
B) (i) $\mathrm { No }$; (ii) Yes
C) (i) No; (ii) No
D) (i) Yes; (ii) No

Question

Determine if each ordered pair is a solution to the given system of inequalities in two variables.
-$$\begin{array} { l } 
x y = 54 \
x ^ { 2 } + y ^ { 2 } = 117
\end{array}$$
(i) $( 6 , - 9 )$; (ii) $( - 9 , - 6 )$
A) (i) Yes; (ii) Yes
B) (i) $\mathrm { No }$; (ii) Yes
C) (i) No; (ii) No
D) (i) Yes; (ii) No

Quizplus · Accepted Answer

For (i) $6 \times -9 = -54$, not 54, and $6^2 + (-9)^2 = 36 + 81 = 117$, so only the second equation is satisfied. For (ii) $(-9) \times (-6) = 54$, and $(-9)^2 + (-6)^2 = 81 + 36 = 117$, so both equations are satisfied.

Determine If Each Ordered Pair Is a Solution to the Given