Questions: Solve the following system of linear equations by graphing: -4x + 2y = -12 -4x + 2y = 24

Transcript text: Solve the following system of linear equations by graphing: \[ \begin{array}{l} -4 x+2 y=-12 \\ -4 x+2 y=24 \end{array} \]

Solution

Solution Steps

Step 1: Convert the equations to slope-intercept form

The given system of linear equations is: \[ \begin{array}{l} -4x + 2y = -12 \\ -4x + 2y = 24 \end{array} \]

First, we convert each equation to slope-intercept form $y = mx + b$.

For the first equation: \[ -4x + 2y = -12 \] Add $4x$ to both sides: \[ 2y = 4x - 12 \] Divide by 2: \[ y = 2x - 6 \]

For the second equation: \[ -4x + 2y = 24 \] Add $4x$ to both sides: \[ 2y = 4x + 24 \] Divide by 2: \[ y = 2x + 12 \]

Step 2: Identify the slope and y-intercept

The slope-intercept forms of the equations are: \[ y = 2x - 6 \] \[ y = 2x + 12 \]

Final Answer

The system of equations in slope-intercept form is: \[ \begin{array}{l} y = 2x - 6 \\ y = 2x + 12 \end{array} \]

{"axisType": 3, "coordSystem": {"xmin": -10, "xmax": 10, "ymin": -10, "ymax": 20}, "commands": ["y = 2x - 6", "y = 2x + 12"], "latex_expressions": ["$y = 2x - 6$", "$y = 2x + 12$"]}

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