
Essential Questions 
EQ 1  How can you solve systems of equations and inequalities? 
EQ 2  How can you use systems of equations and inequalities to model, and then solve, realworld problems? 
Learning Objectives: Systems of Equations and Inequalities 
Solving Linear Systems by Graphing
 Solve a system of linear equations by graphing
 Model reallife problems using a linear system

Solving Linear Systems by Substitution
 Use substitution to solve a linear system
 Model reallife situations using a linear system

Solving Linear Systems by Linear Combinations (elimination)
 Use linear combinations to solve a system of linear equations
 Mode a reallife problem using a linear system

Applications of Linear Systems
 Choose the best method to solve a system of linear equations
 Use a system to model reallife problems

Linear Inequalities
 graph linear inequalities in two variables
 Model reallife problems using linear inequalities

Solving Systems of Linear Inequalities
 Solve a system of linear inequalities by graphing
 Use a system of linear inequalities to model a reallife situation

Specific Skills Developed: 
 Determine whether a specified point is a solution to a system of equations
 Identify linear systems as having one solution, no solution, or infinitely many solutions
 Solve a system of equations by graphing
 Solve a system of equations using substitution
 Solve a system of equations using elimination
 Write a system of equations to model a word problem
 Write a system of equations to model a word problem, solve the system, and verify the solution
 Determine whether a specified point is a solution to an inequality
 Determine whether a specified point is a solution to a system of linear equalities
 Write a system of inequalities to model a word problem
 Write a system of inequalities to model a word problem, solve the system, and verify the solution.

Key Concepts 
Systems Concepts: 
 consistent
 inconsistent
 dependent
 independent
 Linear inequalities, systems of linear inequalities
 Solution of a linear equation
 Solutions of a linear system
 Solutions of a linear inequality
 Solutions of a system of linear inequalities

Methods for solving systems: 
 graphing method
 substitution method
 elimination/linear combination method


Video Examples 
This is a sample problem solved using
three methods  by graphing, by substitution, and by elimination. The elimination method is also sometimes call linear combinations. 
Solve the system by graphing:
4x  y = 1
x + y = x  5
Video Solution

Solve the system by substitution:
4x  y = 1
x + y = x  5
Video Solution

Solve the system by Elimination:
4x  y = 1
x + y = x  5
Video Solution

Sample problems and worked out solutions from Ace100.org 
You have $200 in your bank account and you are going to deposit $16 each week. Your sister’s bank account has $728 and she is going to withdraw $8 per week. In how many weeks will your accounts be equal?
Video Solution

Gabby has $5.65 in dimes and quarters. The number of dimes is 17 less than the number of quarters. How many coins of each type does she have?
Video Solution

The length of a rectangle is 16m less than 3 times the width. The perimeter is 128m. find the width, length, and area of the rectangle.
Video Solution

Ethan's age is 6 times Michelle's age. The sum of their ages is 21. Find the age of each.
Video Solution

The difference of Ethan's age and Bill's age is 13 . The sum of 6 times Ethan's age and 7 times Bill's age is 169. Find the age of each.
Video Solution

There were 304 people at a a fundraiser for the high school girls soccer team. Admission was $14 for each adult and $6 for each student. The total receipts for all ticket sales was $2,376.00. How many adult tickets and student tickets were sold?
Video Solution

Writing and Solving a System of Equations 
 Solve by Graphing Video on Educreations
Five years from now, a father’s age will be three times his son’s age, and 5
years ago, he was seven times as old as his son was. What are their present
ages?


Sample Skills 
Online Practice 
Interactive Practice at Ace100.org .
When you have Javascript enabled you can enter your answers, and/or get help prompts.
Practice these problems until you can solve them using at least two methods.
Tutorials
 How to check if a point is a solution to a specified equation.
Video on VirtualNerd.com

Sample Word Problems 
For each of these word problems, students should be able to:
 Write a system of equations that models the propblem
 Choose an appropriate method for solving the system  graphing, substitution, linear combinations
 Solve the system (for all variables)
 Check the solution (in all equations) algebraically
Samantha has $3.40 in dimes and quarters.
The number of dimes is 8 less than the number of quarters.
How many coins of each type does she have?

A piggy bank has $4.30 in dimes and quarters.
If the number of dimes is 7 more than 2 times the number of quarters,
how many coins of each type are in the piggy bank?

George's age is 5 times Kendell's age.
The sum of their ages is 48. Find the age of each.

The difference of Jimmy's age and Linda's age is 10 years. The sum of 5 times Jimmy's age and 4 times Linda's age is 104. How old is each?

There were 235 people at a movie to raise funds for the drama club.
Admision was $8.00 for each adult and $4.00 for each student.
The total receipts for all tickets was $1504.00.
How many adults and how many students attended?

The length of a rectangle is 11 m less than 5 times the width. The perimeter is 434 m. Find the length and width of the rectangle.

George scored 13 more points than twice as many as Roy did. Their combined score was 40 points. How many points did each score?

The difference of Jen's age and Mark's age is 6 years. The sum of 4 times Jen's age and 3 times Mark's age is 108. How old is each?


