Questions: Solve the following system of linear equations by graphing: -6x + 3y = 27 -6x + 3y = 9 Graph the linear equations by writing the equations in slope-intercept form: y = x + y = x +

Solve the following system of linear equations by graphing: -6x + 3y = 27 -6x + 3y = 9 Graph the linear equations by writing the equations in slope-intercept form: y = x + y = x +
Transcript text: Solve the following system of linear equations by graphing: \[ \begin{array}{l} -6 x+3 y=27 \\ -6 x+3 y=9 \end{array} \] Graph the linear equations by writing the equations in slope-intercept form: \[ \begin{array}{l} y=\square x+\square \\ y=\square x+\square \end{array} \]
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Solution

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Solution Steps

Step 1: Convert the first equation to slope-intercept form

The first equation is \(-6x + 3y = 27\). To convert it to slope-intercept form (\(y = mx + b\)), solve for \(y\):

\[ -6x + 3y = 27 \]

Add \(6x\) to both sides:

\[ 3y = 6x + 27 \]

Divide by 3:

\[ y = 2x + 9 \]

Step 2: Convert the second equation to slope-intercept form

The second equation is \(-6x + 3y = 9\). To convert it to slope-intercept form (\(y = mx + b\)), solve for \(y\):

\[ -6x + 3y = 9 \]

Add \(6x\) to both sides:

\[ 3y = 6x + 9 \]

Divide by 3:

\[ y = 2x + 3 \]

Step 3: Graph the equations

Graph the two equations \(y = 2x + 9\) and \(y = 2x + 3\) on the coordinate plane.

Final Answer

The system of equations has no solution because the lines are parallel and do not intersect.

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