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 System A 5xy=55x+y=5\begin{array}{r} 5 x-y=-5 \\ -5 x+y=-5 \end{array} & \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= \square \end{tabular} \\ \hline System B 3xy6=03x+y=6\begin{aligned} 3 x-y-6 & =0 \\ -3 x+y & =-6 \end{aligned} & \begin{tabular}{l} The system has no solution. The system has a unique solution: (x,y)=(,)(x, y)=(\square, \square) The system has infinitely inany solutions. \\ They must satisfy the following equation: y=y= \square \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: 3xy=63x - y = 6
Now the system is: \begin{align*} 3x - y &= 6 \\ -3x + y &= -6 \end{align*}
Add the two equations to eliminate y y : (3xy)+(3x+y)=6+(6)(3x - y) + (-3x + y) = 6 + (-6)
Simplify: 0=00 = 0
This indicates that the system has infinitely many solutions. To find the relationship between x x and y y , solve one of the equations for y y : 3xy=6    y=3x63x - y = 6 \implies y = 3x - 6
Thus, the solutions satisfy the equation y=3x6 y = 3x - 6 .
System A: The system has no solution.
System B: The system has infinitely many solutions. They must satisfy the equation y=3x6 y = 3x - 6 .

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