Solve the system by the method of substitution. $$\left\{ \begin{aligned}
x ^ { 2 } - 12 y ^ { 2 } & = 144 \
x ^ { 2 } + y ^ { 2 } & = 1
\end{aligned} \right.$$
A) $( 0,12 ) , ( 0 , - 12 )$
B) $\left( 12 , \frac { 1 } { 12 } \right) , \left( 12 , - \frac { 1 } { 12 } \right) , \left( - 12 , \frac { 1 } { 12 } \right) , \left( - 12 , - \frac { 1 } { 12 } \right)$
C)(12 $2 \sqrt { 3 }$ , 12 $\sqrt { 13 }$ ), (12 $2 \sqrt { 3 }$ , 12 $\sqrt { 13 }$ ), ( 12 $2 \sqrt { 3 }$ ,12 $\sqrt { 13 }$ ), ( 12 $2 \sqrt { 3 }$ , 12 $\sqrt { 13 }$ )
D) $\left( \frac { 155 } { 11 } , - \frac { 144 } { 11 } \right)$
E)no solution exists

Question

Quizplus · Accepted Answer

The system of equations given is inconsistent when solved by substitution, as the equations represent a hyperbola and a circle that do not intersect.

Solve the System by the Method of Substitution {x2−12y2=144x2+y2=1\left\{ \begin{aligned}x ^ { 2 } - 12 y ^ { 2 } & = 144 \\x ^ { 2 } + y ^ { 2 } & = 1\end{aligned} \right.{x2−12y2x2+y2​=144=1​

Solve the System by the Method of Substitution $\left\{ \begin{aligned}x ^ { 2 } - 12 y ^ { 2 } & = 144 \\x ^ { 2 } + y ^ { 2 } & = 1\end{aligned} \right.$