\( 3 x+2 y=27 \) and \( y=\frac{28-2 x}{3} \)

These two equations represent a system of linear equations. The first equation, \( 3x + 2y = 27 \), can be visualized as a straight line in a 2D coordinate plane, where \( x \) and \( y \) are the axes. Meanwhile, the second equation, \( y=\frac{28-2x}{3} \), is already in slope-intercept form, making it easier to plot. Finding the intersection of these lines will give you the solution to the system, which can provide insights into various fields such as economics or engineering, where resource allocation is essential. When solving for the intersection of these lines, a common mistake is to confuse the operations with fractions. It’s crucial to carefully manipulate each equation step by step to avoid errors. Always double-check your expressions before substituting them into the other equation! This not only saves time but also ensures accuracy. A handy tip is to isolate one variable in both equations before setting them equal to each other for solving. Happy solving!