Questions: Solve graphically. 3x - y = 4 -9x + 3y = -15

Solve graphically. 3x - y = 4 -9x + 3y = -15
Transcript text: er 6 Quiz Solve graphically. \[ \begin{array}{l} 3 x-y=4 \\ -9 x+3 y=-15 \end{array} \]
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Solution

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Solution Steps

Step 1: Rewrite the Equations in Slope-Intercept Form

To solve the system of equations graphically, we first rewrite each equation in the slope-intercept form, \(y = mx + b\).

  1. For the first equation \(3x - y = 4\): \[ y = 3x - 4 \]

  2. For the second equation \(-9x + 3y = -15\): \[ 3y = 9x - 15 \\ y = 3x - 5 \]

Step 2: Graph the Equations

Next, we graph the two equations on the same coordinate plane.

  1. Graph of \(y = 3x - 4\):

    • The y-intercept is \(-4\), so the line crosses the y-axis at \((0, -4)\).
    • The slope is \(3\), which means for every 1 unit increase in \(x\), \(y\) increases by 3 units.

  2. Graph of \(y = 3x - 5\):

    • The y-intercept is \(-5\), so the line crosses the y-axis at \((0, -5)\).
    • The slope is also \(3\).
Step 3: Analyze the Graph

Since both lines have the same slope but different y-intercepts, they are parallel and will never intersect. Therefore, there is no solution to this system of equations.

Final Answer

The system of equations has no solution because the lines are parallel.

\[ \boxed{\text{No solution}} \]

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