Solving systems of equations underpins much of advanced algebra, especially linear algebra. Developing an intuition for the kinds and descriptions of solutions is key for success in those later courses. This intuition is exactly what...

Systems of parallel lines have no solution. Pupils work examples to discover that lines with the same slope and different y-intercepts are parallel. The 27th segment of 33 uses this discovery to develop a proof, and the class determines...

This instructional activity is all about systems of equations and their graphs. Algebra learners create and solve systems of equation using tables and graphing. They identify the point of intersection of a system of equation, and...

The class solves systems of linear inequalities. They graph lines and identify the point of intersection.They graph lines and identify the boundary that represent the solution and solution set.

The brother-sister pair Carlos and Clarita need your class's help in developing their new pet sitting business. Through a variety of scenarios and concerns presented to the siblings, the learners thoroughly explore systems of equations...

Explore methods for solving linear systems with your classes and introduce learners to using matrices as a viable method. Scholars are able to recognize situations where matrices are the efficient method of solving. Application...

Here is an introduction to solving simultaneous linear equations. Start by drawing a line through two points. Create a second line which goes through the intersecting point. Background knowledge of how to find the equation of a line and...

Students explore the concept of solving systems of equations. In this solving systems of equations activity, students watch YouTube videos about how to solve systems by graphing and by elimination. Students use an interactive website to...

How many different ways can three planes intersect? The interactive provides three movable planes. Pupils manipulate the planes to determine the number of solutions possible based upon their intersections.

Systems of equations and inequalities model contextual situations. A set of 12 lessons build a solid understanding of writing and solving systems of equations and inequalities using a variety of methods. The module is the fifth in a...

Lets keep the system working and show learners the three ways to solve linear systems of equations. Each method includes step-by-step instructions to work their way through the problem. The same problem is used for each method to show...

Eleventh graders solve systems of equation. In this algebra lesson, 11th graders find the point of intersection of two lines if there is any, using algebra and graphing. They use substitution and linear combination to find the solution...

Learners find the common point of a linear and quadratic system given a graph of the system. Then they find a specific point located only on the parabola.

This worksheet and tutorial explores solving more complex polynomials by graphing each side separately and finding the point of intersection, identifying the sum and differences of cubes, and solving higher degree polynomials by using...

This is a lengthy overview PowerPoint that defines, explains, shows examples, and has practice problems about points, lines and planes.  The class will need to write many notes and there is an example of how to set up in the Cornell...

The slope makes a difference. Given an equation of a circle and point, scholars determine the relationship of the slope of a line through the point and the number of intersections with the circle. After graphing the relationship, pupils...

Mathematically shoot down an incoming missile. Given information about the Cuban Missile Crises, learners calculate the equation of the trajectory of an imaginary missile launched from Cuba toward Washington, D.C. Scholars determine the...

Investigate linear quadratic systems and pose this question: Do all linear quadratic systems have two solutions? Do they all have a solution? Learners solve systems of equations through graphing. They indicate the points of intersection...

This activity consists of three exercises in which learners sketch the graphs of various power functions on the same axes. They use their sketches to make comparisons and observations which lead to generalizations about the graphs...

Explore nonlinear systems through graphs and algebra. High schoolers begin by examining the different types of quadratic functions and their possible intersections. They then use algebraic methods to solve systems containing various...

Keep young mathematicians on point with this coordinate plane worksheet. From plotting ordered pairs to identifying the quadrant and coordinates of specific points, this resource covers all the basic skills students need to have...

It's time to show off what they learned! The final lesson in the series is a review worksheet on the topics learned throughout the unit. Scholars solve systems of equations using graphic and algebraic methods, solve system-based word...

What do you get when you cross a circle and a line? One, two, or maybe no solutions! Teach learners to find solutions of quadratic and linear systems. Connect the visual representation of the graph to the abstract algebraic methods. 

Students calculate the distance between two points. In this geometry lesson plan, students define the meaning of the distance between parallel lines. They find the point of intersection of other lines.