Solve the system by graphing. \( \begin{array}{l}y-3=3 x \\ y+3=3 x\end{array} \)

To solve the system by graphing, we first need to rewrite both equations in slope-intercept form (y = mx + b): 1. For the first equation: \( y - 3 = 3x \) ⇒ \( y = 3x + 3 \) 2. For the second equation: \( y + 3 = 3x \) ⇒ \( y = 3x - 3 \) Now, we can graph both equations. The first line, \( y = 3x + 3 \), has a y-intercept at (0, 3) and a slope of 3, meaning it rises 3 units for every 1 unit it moves to the right. The second line, \( y = 3x - 3 \), has a y-intercept at (0, -3) with the same slope, so it will be parallel to the first line. Since the lines are parallel and never intersect, this system has no solution! Now, speaking of graphing, did you know that the method can be visualized in many cool ways? Using graphing software or apps can instantly show you where curves and lines lie. Also, if you're interested in delving deeper into related topics, exploration of systems of equations through substitution or elimination methods can be intriguing, as these techniques provide structured approaches to finding solutions, especially when lines intersect!