Questions: Solve the system by graphing. 3x - 2y = 12 6x - 4y = -24

Transcript text: Solve the system by graphing. \[ \begin{array}{l} 3 x-2 y=12 \\ 6 x-4 y=-24 \end{array} \]

Solution

Solution Steps

Step 1: Identify the Equations

The given system of equations is: \[ \begin{align_} 3x - 2y &= 12 \\ 6x - 4y &= -24 \end{align_} \]

Step 2: Simplify the Second Equation

Notice that the second equation can be simplified by dividing all terms by 2: \[ 3x - 2y = -12 \]

Step 3: Compare the Equations

Now we have: \[ \begin{align_} 3x - 2y &= 12 \\ 3x - 2y &= -12 \end{align_} \] These two equations are parallel lines with no points of intersection, indicating that the system has no solution.

Final Answer

The system of equations has no solution.

{"axisType": 3, "coordSystem": {"xmin": -10, "xmax": 10, "ymin": -10, "ymax": 10}, "commands": ["y = (3/2)x - 6", "y = (3/2)x + 6"], "latex_expressions": ["$3x - 2y = 12$", "$3x - 2y = -12$"]}

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