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Understanding how to graph linear equations is essential for solving a system of equations. The standard form of a linear equation is typically expressed as \( Ax + By = C \). However, for graphing purposes, it's often more practical to use the slope-intercept form, \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept, the point where the line crosses the y-axis.

In the given exercise, the equations were reformatted to this user-friendly form. Once reformatted, you can plot the equation by choosing values for x, calculating the corresponding y values, and then placing those points on the graph. For a straight line, only two points are needed to determine the line because a straight line is the shortest distance between two points.

Learning to graph these equations accurately is crucial because visual representation helps verify solutions and understand the relationships between equations in a system. It's also a good practice to label your axes, plot points with precision, and draw the lines using a straight edge.

The solution of a system of equations refers to the set of values that satisfies all equations in the system simultaneously. In the context of linear equations, this is generally the point where the lines intersect on a graph. When dealing with a system, it's important to find the values for the variables that make all the equations true at the same time.

For example, if you're given a system consisting of two equations with the same two variables, you'll be looking for a pair of x and y values that satisfy both equations. This forms the cornerstone of algebra and helps us solve real-world problems with multiple constraints. In complex systems where graphing may not be feasible or precise, algebraic methods such as substitution or elimination are employed to find the solution. However, graphing provides a visual check that can reinforce algebraic findings.

The point of intersection is precisely where two or more lines on a graph cross each other. This single point represents the set of values that solves each of the equations involved. In a system with two variables, such as the one in the exercise, the point of intersection is the ordered pair \((x, y)\) that is the solution to the system.

While graphically a common point of intersection can often be identified by eye, it is always good practice to solve the equations algebraically for confirmation. If lines do not intersect, they may be parallel, indicating that no solution exists that satisfies all the equations, or they may overlap entirely, implying an infinite number of solutions. For the given problem, one would investigate the point(s) of intersection by checking if there is a consistent ordered pair when solving the equations pairwise. The point of intersection is where the logic of the system crystallizes into an exact answer that tells the story of the relationship between the equations.