In this activity, students will recognize a system of equations, determine solutions graphically, and verify solutions algebraically.
- Students will recognize a system of equations.
- Students will know the definition of a system of an equation.
- Students will determine solutions to a system of equations graphically.
- Students will verify solutions to a system algebraically.
- Students will understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.
- Students will solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations.
- System of Equations
- Solving a System of Equations
- Point of Intersection
- Parallel lines
About the Lesson
This lesson involves definitions of a system of equations and solutions to a system of equations.
As a result, students will:
- Examine a graph of a system of two equations and two unknowns. They will be able to drag a point along the x-axis and as they do, corresponding points will move along the two graphs of the equations.
- Recall that any point on a particular equation is a solution to that given equation, but should notice that to solve a system of equations, they are looking for a solution that simultaneously solves both equations.