Questions: Solve the system of linear equations by graphing. 6x - y = 9 1/3 y = -3 + 2x

Solve the system of linear equations by graphing. 6x - y = 9 1/3 y = -3 + 2x
Transcript text: Solve the system of linear equations by graphing. \[ \left\{\begin{array}{l} 6 x-y=9 \\ \frac{1}{3} y=-3+2 x \end{array}\right. \]
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Solution

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Solution Steps

Step 1: Solve the first equation for \( y \)

The first equation is:

\[ 6x - y = 9 \]

Solve for \( y \):

\[ y = 6x - 9 \]

Step 2: Solve the second equation for \( y \)

The second equation is:

\[ \frac{1}{3}y = -3 + 2x \]

Multiply both sides by 3 to solve for \( y \):

\[ y = 6x - 9 \]

Step 3: Identify the solution of the system

Both equations simplify to the same line:

\[ y = 6x - 9 \]

This means the system has infinitely many solutions, as both equations represent the same line.

Final Answer

The system of equations has infinitely many solutions, as both equations represent the same line: \( y = 6x - 9 \).

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