Solving Systems by Graphing

Given two linear equations in slope-intercept form, solve the system of equations by graphing to find the intersection point.

To solve a system of linear equations means to find the point(s) where the graphs of the equations intersect. When solving by graphing, it's essential to understand that each equation represents a line, and the solution to the system is the point where these lines meet. The intersection point represents the values that satisfy both equations simultaneously. This visual method not only provides the solution but also offers insight into the nature of the system, such as whether there are no solutions or infinitely many solutions which occur when the lines are parallel or coincident, respectively.

Graphing is a helpful technique that reinforces the concept of what a solution to a system of equations represents. While solving algebraically using substitution or elimination is usually more precise, graphing provides a unique, intuitive insight. It's particularly useful for small systems and serves as a foundational skill that supports understanding more advanced algebraic techniques. When graphing, ensure the lines are accurately drawn to scale to identify the correct intersection point, especially when estimating solutions.