Unit Resources

Unit: Systems of Equations and Inequalities
  
Essential Questions
EQ 1How can you solve systems of equations and inequalities?
EQ 2How can you use systems of equations and inequalities to model, and then solve, real-world problems?

Learning Objectives: Systems of Equations and Inequalities
    Solving Linear Systems by Graphing
  • Solve a system of linear equations by graphing
  • Model real-life problems using a linear system
    Solving Linear Systems by Substitution
  • Use substitution to solve a linear system
  • Model real-life situations using a linear system
    Solving Linear Systems by Linear Combinations (elimination)
  • Use linear combinations to solve a system of linear equations
  • Mode a real-life 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 real-life problems
    Linear Inequalities
  • graph linear inequalities in two variables
  • Model real-life 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 real-life 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
Solving Systems Using Substitution
1)
x + y = 3
2x - y = 0
Video Solution
2)
x - 3y = -14
x - y = -2
Video Solution
3)
6x - 5y = 3
x - 9y = 25
white board solution

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 sisterís 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 fatherís age will be three times his sonís 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?