QuestionTwo systems of equations are given below. For each system, choose the best description of its solution. If applicable, give the solution. \begin{tabular}{|c|c|} \hline System A & \begin{tabular}{l} The system has no solution. The system has a unique solution: The system has infinitely many solutions. \\ They must satisfy the following equation: \end{tabular} \\ \hline System B & \begin{tabular}{l} The system has no solution. The system has a unique solution: The system has infinitely inany solutions. \\ They must satisfy the following equation: \end{tabular} \\ \hline \end{tabular}
Studdy Solution
Analyze System B:
The system of equations is:
\begin{align*}
3x - y - 6 &= 0 \\
-3x + y &= -6
\end{align*}
Rearrange the first equation:
Now the system is:
\begin{align*}
3x - y &= 6 \\
-3x + y &= -6
\end{align*}
Add the two equations to eliminate :
Simplify:
This indicates that the system has infinitely many solutions. To find the relationship between and , solve one of the equations for :
Thus, the solutions satisfy the equation .
System A: The system has no solution.
System B: The system has infinitely many solutions. They must satisfy the equation .
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