Questions: Graph the system of equations. y=-1.5x+2 3x+2y=4

Transcript text: Graph the system of equations. \[ \begin{array}{l} y=-1.5 x+2 \\ 3 x+2 y=4 \end{array} \]

Solution

Solution Steps

Step 1: Solve the first equation for $ y $

The first equation is already solved for $ y $: \[ y = -1.5x + 2 \]

Step 2: Solve the second equation for $ y $

The second equation is: \[ 3x + 2y = 4 \]

To solve for $ y $, subtract $ 3x $ from both sides: \[ 2y = 4 - 3x \]

Now, divide by 2: \[ y = 2 - \frac{3}{2}x \]

Step 3: Identify the equations to be plotted

The equations to be plotted are:

$ y = -1.5x + 2 $
$ y = 2 - \frac{3}{2}x $

Final Answer

The system of equations to be graphed is:

$ y = -1.5x + 2 $
$ y = 2 - \frac{3}{2}x $

{"axisType": 3, "coordSystem": {"xmin": -10, "xmax": 10, "ymin": -10, "ymax": 10}, "commands": ["y = -1.5x + 2", "y = 2 - (3/2)x"], "latex_expressions": ["$y = -1.5x + 2$", "$y = 2 - \\frac{3}{2}x$"]}

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