Solve the system by using any method.
-$$\begin{array} { l }
2 ^ { x } + 2 ^ { y } = 18 \
4 ^ { x } - 2 ^ { y } = - 12
\end{array}$$
A) $\{ ( 1,4 ) \}$
B) $\{ ( 4,1 ) \}$
C) $\left\{ \left( 0 , \log _ { 2 } 18 \right) \right\}$
D) $\left\{ \left( \log _ { 2 } 18,0 \right) \right\}$

Question

Solve the system by using any method.
-$$\begin{array} { l } 
2 ^ { x } + 2 ^ { y } = 18 \
4 ^ { x } - 2 ^ { y } = - 12
\end{array}$$
A) $\{ ( 1,4 ) \}$
B) $\{ ( 4,1 ) \}$
C) $\left\{ \left( 0 , \log _ { 2 } 18 \right) \right\}$
D) $\left\{ \left( \log _ { 2 } 18,0 \right) \right\}$

Quizplus · Accepted Answer

Adding the two equations: $2^x + 2^y + 4^x - 2^y = 18 - 12$, simplifies to $2^x(1 + 2^x) = 6$. Substituting $2^x = 2$ and $2^y = 16$ solves the system, giving $x = 1$ and $y = 4$.

Solve the System by Using Any Method 2x+2y=184x−2y=−12\begin{array} { l } 2 ^ { x } + 2 ^ { y } = 18 \\4 ^ { x } - 2 ^ { y } = - 12\end{array}2x+2y=184x−2y=−12​

Solve the System by Using Any Method $\begin{array} { l } 2 ^ { x } + 2 ^ { y } = 18 \\4 ^ { x } - 2 ^ { y } = - 12\end{array}$