Download Chapter 6: Systems of Linear Equations and

Mrs. Branson
Algebra 1
Chapter 6: Systems of Linear Equations and Inequalities
Chapter Objectives:
Lesson 6.1: Graphing Systems of Equations
 Determine the number of solutions a system of linear equations has, if any
 HW: Pg. 336 # 10–20 Evens and #26, 30
Lesson 6.2: Substitution
 Solve systems of equations by using substitution
 HW: Pg. 345 – 346 #10–26 Evens
Lesson 6.3: Elimination Using Addition and Subtraction
Lesson 6.4: Elimination Using Multiplication
 Solve systems of equations by using elimination with addition, subtraction,
and multiplication
 HW: Pg. 352 #14-30 Evens and Pg. 358 #14-24 Evens
Lesson 6.5: Applying Systems of Linear Equations
 Determine the best method for solving systems of equations
 Apply systems of equations
 HW: Pg. 365-366 #6-22 Evens
Lesson 6.6: Organizing Data Using Matrices
 Organize data in matrices
 Perform matrix operations
 HW: Worksheet
Lesson 6.7: Using Matrices to Solve Systems of Equations
 Write systems of equations as augmented matrices
 Solve systems of equations by using elementary row operations (row
reduction)
 HW: Practice Test Part 1
Standards:
A.REI.6: Solve systems of linear equations exactly and approximately (e.g. with graphs),
focusing on pairs of linear equations in two variables.
A.REI.7: Solve a simple system consisting of a linear equation and a quadratic equation in two
variables algebraically and graphically. For example, find the points of intersection between y =
-3x and the circle x2 + y2 = 3.
A.REI.5: Prove that given a system of two equations in two variables replacing one equation by
the sum of that equation and a multiple of the other produces a system with the same solutions.
A.REI.8: Represent a system of linear equations as a single matrix equation in a vector
variable.
A.REI.9: Find the inverse of a matrix if it exists and use it to solve systems of linear equations
(using technology for matrices of dimension 3 x 3 or better)
Lesson 6.1: Graphing Systems of Equations
 Determine the number of solutions a system of linear equations has, if any
 HW: Pg. 336 # 10–20 Evens and #26, 30
Term

Meaning
Two or more equations with the same
variables
Example:


A system with at least one solution
Graphs intersect at one point or are the
same line

A consistent system with exactly one
solution

A consistent system with unlimited
solutions that satisfy both equations


A system with no solution
The graphs are parallel
Possible Solutions
Number of Solutions
Terminology
Graph
Examples:
Consistent and
Independent
Consistent and
Dependent
Inconsistent
Lesson 6.2: Substitution
 Solve systems of equations by using substitution
 HW: Pg. 345 – 346 #10–26 Evens
An algebraic method to find an exact
solution to a system of equations
Steps for Solving a System of Equations using Substitution
1.
When necessary, ________________ at least one equation for ___________________________
2.
____________________ the resulting expression from Step 1 into the other equation to
_________________ the variable. Then _____________________________________________
3.
____________________ the value from Step 2 into ____________________________________
and solve for the other variable.
4.
Write the ____________________ as an _____________________________________________
Examples:
𝑦 = 5𝑥 + 1
4𝑥 + 𝑦 = 10
𝑦 = 3𝑥 − 2
𝑦 = 2𝑥 − 5
−1 = 2𝑥 − 𝑦
8𝑥 − 4𝑦 = −4
3𝑥 + 𝑦 = −5
6𝑥 + 2𝑦 = 10
In 2000, the demand for nurses was 2,000,000, while the supply was only 1,890,000. The
projected demand for nurses in 2010 was 2,820,000,000, while the supply was only projected to
be 1,810,000.
a. Define the variables, and write equations to represent these situations
b. Use substitution to determine during which year the supply of nurses was equal to the
demand.