Systems of Equations
|Overview of Objectives, students should be
1. Determine if a given ordered
pair is a solution to a
|Main Overarching Questions:
1. When is an ordered pair a solution of a system?
2. How do you solve systems of equations by graphing?
3. How do you solve systems of equations by algebraic methods ?
4. Compare and contrast the methods of solving systems for efficiency and accuracy.
5. How do you determine when a system has no solution or infinitely many solutions?
||Activities and Questions to ask
|• Determine if a given ordered pair is a solution
system of linear equations.
|1. Present two linear equations and
have students substitute an ordered pair into x and y.
What is meant by the term “solution to an equation”? Does the ordered pair create true
or false statements? Is this point a solution for both of these equations?
. When is an ordered a solution of a system of linear equations?
|• Solve systems of linear equations using
| Group activity or teacher directed:
1. Students will graph 3 systems of linear equations:
a) a pair of intersecting lines b) a pair of
2. Direct students to compare the three systems:
a) describe the type of lines b)describe how
3. Groups may present their results.
4. Summarize using 3‐column note format.
|• Solve systems of linear equations by
|1. What does substitution mean? What
can be substituted without changing the solution of an
2. If 2 equations are solved for y like y = 2x – 1 and y = x + 4, can you say that 2x‐1 = x + 4. Why or why not? Now that you can solve for x, how can you find y?
For students who struggle with substitution method, try the above method.
3. Demonstrate technique of solving one equation
for a variable. How can we use
4. How does this help us solve the system? How do you find the second variable?
5. What happens if you substitute into the wrong
|• Solve systems of linear equations by addition
|1. How do you add two equations ? What
parts can you add?
2. Ask students to add
two given equations (where a variable will cancel). How does this help
3. Ask students to add two given equations where a
variable does not cancel? Does this help us
4. How can we change an equation so that a
variable will cancel when we add? IF we change
5. Introduce or reemphasize term: equivalent equations
|• Select the most efficient method for solving a
of linear equations.
• Identify systems that
have no solution or infinitely
|1. Have students compare/contrast the
3 methods of solving a system. Do lines always
intersect at integer points? Can you always read the coordinates of the intersection on a
graph? Can you determine fraction solutions when solving using algebraic methods.
2. Ask students to make a conclusion about the efficiency and accuracy of each method.
3. Give students a system with no solution and ask
them to use either the substitution or
4. Give students a system with infinitely many
solutions and ask them to solve using addition or