Unit 4 lesson 9
Lesson 9: Solving Systems of Equations by Graphing
In this lesson, we will learn how to solve systems of linear equations by graphing.
A system of equations is a set of two or more equations with the same variables. In solving a system of equations, we find the values of the variables that satisfy all of the equations simultaneously. One way to solve a system of equations is by graphing the equations on the same coordinate plane and finding the point (or points) where the graphs intersect.
To solve a system of equations by graphing, follow these steps:
1. Write down the given system of equations. Each equation should be in the form y = mx + b, where m represents the slope and b represents the y-intercept.
2. Graph each equation on the same coordinate plane. Start by plotting the y-intercept (b) on the y-axis, and then use the slope (m) to find additional points on the line. Repeat this process for each equation in the system.
3. Identify the point (if any) where the graphs intersect. This point represents the solution to the system of equations.
4. Check your solution by substituting the values of the variables into each equation. The solution should satisfy all of the equations in the system.
If the graphs do not intersect or the system has no solutions, it means that the given equations are parallel or represent the same line. If the graphs coincide and overlap, it means that the system has infinitely many solutions.
It's important to note that solving systems of equations by graphing can be time-consuming and less accurate compared to other methods, especially for systems with non-linear equations. However, it can provide a visual representation of the solutions and is a good starting point for understanding systems of equations.