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The system has no solution. $\newline$ The system has a unique solution: $\newline$ $(x,y)=(\square,\square)$ $\newline$ \begin{cases}x+2y=8\-x-2y=8\end{cases} $\newline$ The system has infinitely many solutions. $\newline$ They must satisfy the following equation: $\newline$ y=

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Find trigonometric ratios of special angles

Full solution

Q. The system has no solution.

\newline

The system has a unique solution:

\newline

(x,y)=(\square,\square)

\newline

\begin{cases}x+2y=8\-x-2y=8\end{cases}

\newline

The system has infinitely many solutions.

\newline

They must satisfy the following equation:

\newline

y=

Analyze Equations: Analyze the system of equations to determine if there is a solution. $\newline$ The system of equations is: $\newline$ $1$ . $x + 2y = 8$ $\newline$ $2$ . $-x - 2y = 8$ $\newline$ We can add the two equations together to see if they are consistent or inconsistent. $\newline$ Adding equation $1$ and equation $2$ gives us: $\newline$ $(x + 2y) + (-x - 2y) = 8 + 8$ $\newline$ This simplifies to: $\newline$ $0 = 16$ $\newline$ Since $0 \neq 16$ , this indicates that the system is inconsistent.
Determine Consistency: Conclude the type of solution the system has based on the inconsistency found in Step $1$ . $\newline$ Because we have found an inconsistency, the system has no solution. There is no need to proceed further with solving for $x$ or $y$ since the equations contradict each other.

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