Warm Up #6 1. Let a = 4, b = – 5, c = – 2, and d = 7. Find ad – bc.

Slides:



Advertisements
Similar presentations
Example 1 Matrix Solution of Linear Systems Chapter 7.2 Use matrix row operations to solve the system of equations  2009 PBLPathways.
Advertisements

System of Equations A set of two or more equations with the same variables. To solve a system of equations means to find values for the variables in the.
Use an inverse matrix to solve the linear system.
Do Now Pass out calculators. Solve the following system by graphing: Graph paper is in the back. 5x + 2y = 9 x + y = -3 Solve the following system by using.
Section 8.3 – Systems of Linear Equations - Determinants Using Determinants to Solve Systems of Equations A determinant is a value that is obtained from.
Chapter 3 – Linear Systems
Objective - To graph linear equations using x-y charts. One Variable Equations Two Variable Equations 2x - 3 = x = 14 x = 7 One Solution.
6.8 –Systems of Inequalities. Just like systems of equations, but do the inequality part!
Thinking Mathematically Algebra: Graphs, Functions and Linear Systems 7.3 Systems of Linear Equations In Two Variables.
7.1 SOLVING SYSTEMS BY GRAPHING The students will be able to: Identify solutions of linear equations in two variables. Solve systems of linear equations.
Math 71A 3.1 – Systems of Linear Equations in Two Variables 1.
6.3 – Solving Systems of Linear Equations by Elimination.
CHAPTER 7-1 SOLVING SYSTEM OF EQUATIONS. WARM UP  Graph the following linear functions:  Y = 2x + 2  Y = 1/2x – 3  Y = -x - 1.
Matrix Solutions to Linear Systems. 1. Write the augmented matrix for each system of linear equations.
Solving Systems of 3 or More Variables Why a Matrix? In previous math classes you solved systems of two linear equations using the following method:
4-8 Augmented Matrices and Systems
Math /4.2/4.3 – Solving Systems of Linear Equations 1.
Solving Linear Inequalities Lesson 5.5 linear inequality: _________________________________ ________________________________________________ solution of.
Sullivan Algebra and Trigonometry: Section 12.3 Objectives of this Section Write the Augmented Matrix of a System of Linear Equations Write the System.
10.3 Systems of Linear Equations: Matrices. A matrix is defined as a rectangular array of numbers, Column 1Column 2 Column jColumn n Row 1 Row 2 Row 3.
Linear Systems of Equations Section 3.1. What is a “system” of equations?
Systems of Linear Equations in Two Variables. 1. Determine whether the given ordered pair is a solution of the system.
Solving Linear Systems by Substitution
RECOGNIZING INCONSISTENT LINEAR SYSTEMS. What is an Inconsistent Linear System?  An inconsistent linear system is a system of equations that has no solutions.
SystemsOfInequalities. 7-1 Solving Systems by Graphing What is a system of linear equations? “SOLUTION” No solution Infinitely Many Solutions Page 342.
Differential Equations Linear Equations with Variable Coefficients.
6-1 Solving Systems by Graphing 6-2 Solving Systems by Substitution 6-3 Solving Systems by Elimination 6-4 Solving Special Systems 6-5 Applying Systems.
WARM UP GRAPHING LINES Write the equation in slope- intercept form and then Graph. (Lesson 4.7) 1.3x + y = 1 2.x + y = 0 3.y = -4 3.
GUIDED PRACTICE for Example – – 2 12 – 4 – 6 A = Use a graphing calculator to find the inverse of the matrix A. Check the result by showing.
Solving Systems By Graphing. Warm – Up! 1. What are the 2 forms that equations can be in? 2. Graph the following two lines and give their x-intercept.
Chapter 8 Systems of Linear Equations in Two Variables Section 8.3.
SYSTEMS OF LINEAR EQUATIONS College Algebra. Graphing and Substitution Solving a system by graphing Types of systems Solving by substitution Applications.
5.1 Solving Systems of Equations Objectives: --To identify a system of equations --To determine if a point is a solution to a system --To use graphing.
TODAY IN ALGEBRA 2.0…  Review: Solving Linear Systems by Graphing  Learning Goal 1: 3.2 Solving Linear Systems by Substitution with one equation solved.
3.5 Solving systems of equations in three variables Main Ideas Solve systems of linear equations in three variables. Solve real-world problems using systems.
Algebra 3 5.1/2 Systems of Linear Equations/Matrices.
Use Inverse Matrices to Solve Linear Systems
3.3 – Solving Systems of Inequalities by Graphing
10.3 Solving Linear Systems
The Inverse of a Square Matrix
8.7Systems of Linear Equations – Part 1
Linear Systems November 28, 2016.
Solving System of Linear Equations
Systems of Equations Lesson 41: Solve by using a matrix
Solving Systems in 3 Variables using Matrices
Larger Systems of Linear Equations
Solving Linear Equations
6-2 Solving Systems using Substitution
Warm-Up 2-1.
Warm-up: Simplify: Solve: 1) (3x + 2y) – 2(x + y) 2) y2 + (y – 2)2 = 2
Solve a system of linear equation in two variables
7.1 System of Equations Solve by graphing.
Solutions to Systems of Equations
Warm Up Graph y = 4x and 16, $10’s and 7 $20’s.
Systems of Linear Equations in Two Variables
Matrix Solutions to Linear Systems
Systems of Equations Solving by Graphing.
9.6 Solving Systems of Equations by Graphing
6 minutes Warm-Up Find each product..
5.1 Solving Systems of Equations by Graphing
Warm Up Graph y = 4x and 16, $10’s and 7 $20’s.
Systems of Equations Solve by Graphing.
Warm-Up 1) Sketch a graph of two lines that will never intersect.
Warm Up Check to see if the point is a solution for the
4 minutes Warm-Up Solve and graph. 1) 2).
Objective: Students will solve systems by graphing
Systems Warm-Up Solve each linear system. x + 7 = y -4x + 2 = y
Lesson 0 – 8 Systems of Linear Equations
4 minutes Warm-Up 1) Determine whether (-1,7) is a solution of the system. 3x – y = -10 -x + y = 8 2) Solve for x where 5x + 3(2x – 1) = 5.
Warm- Up: Solve by Substitution
Presentation transcript:

Warm Up #6 1. Let a = 4, b = – 5, c = – 2, and d = 7. Find ad – bc. (4)(7) – (-5)(-2) 28 – 10 18 2. Solve the linear system. 2x – 3y = 4 –x – 2y = –9 2x – 3(2) = 4 2( ) 2x – 3y = 4 –2x – 4y = –18 2x – 6 = 4 2x = 10 x = 5 -7y = -14 (5 , 2) y = 2

= 1(3*6 – 2*4) – 1(-1*6 – 0*4)+ 2(-1*2 – 0*3) 1(18 – 8) – 1(-6) +2(-2) = 10 +6 – 4 = 12

EXAMPLE 1 Evaluate determinants Evaluate the determinant of the matrix. a. 5 4 3 1 b. 2 3 4 1 – SOLUTION

Solve a system of equations in three variables using the graphing calculator APPS  PlySmlt2  #2  Enter the equation in augmented matrix form

Use the PolySmlt2 application on your calculator to solve: Gives: X1=3-2x3 Means: INFINITE # of Solutions X = -3 Y = 4 Z = 1 No solution