Math  /  Algebra

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 \begin{tabular}{l} System A \\ \begin{tabular}{r} x+2y=8-x+2 y=8 \\ x2y=8x-2 y=8 \end{tabular} \end{tabular} & \begin{tabular}{l} The system has no solution. \\ The system has a unique solution: \\ (x,y)=(,)(x, y)=(\square, \square) \\ The system has infinitely many solutions. \\ They must satisfy the following equation: \\ y=y= \end{tabular} \\ \hline \begin{tabular}{l} System B \\ \begin{aligned}x-3 y & =9 \\ -x+3 y & =-9\end{aligned} \end{tabular} & \begin{tabular}{l} The system has no solution. \\ The system has a unique solution: \\ (x,y)=(x, y)= \\ The system has infinitely many solutions. \\ They must satisfy the following equation: \\ y=y= \end{tabular} \\ \hline \end{tabular}

Studdy Solution
Express one variable in terms of the other for System B. Let's solve for xx in terms of yy using the first equation. x3y=9    x=9+3yx - 3y = 9 \implies x = 9 + 3y The solutions to System B must satisfy x=9+3yx = 9 + 3y.
_SOLUTION_: - For System A: - The system has no solution.
- For System B: - The system has infinitely many solutions. - They must satisfy the following equation: x=9+3yx = 9 + 3y.

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