Algebra and Trigonometry by Cynthia Y. Young, © 2007 John Wiley and Sons. All rights reserved. Solving Systems of Equations.

Slides:



Advertisements
Similar presentations
Solve a System Algebraically
Advertisements

Solving a System of Equations by ELIMINATION. Elimination Solving systems by Elimination: 1.Line up like terms in standard form x + y = # (you may have.
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.
3.5 Solving systems of equations in 3 variables
7 = 7 SOLUTION EXAMPLE 1 Check the intersection point Use the graph to solve the system. Then check your solution algebraically. x + 2y = 7 Equation 1.
Thinking Mathematically Algebra: Graphs, Functions and Linear Systems 7.3 Systems of Linear Equations In Two Variables.
Solving Systems of Equations: Elimination Method.
TODAY IN ALGEBRA…  Learning Goal: 7.2 You will solve systems of linear equations by Substitution  Independent Practice.
3x – 5y = 11 x = 3y + 1 Do Now. Homework Solutions 2)2x – 2y = – 6 y = – 2x 2x – 2(– 2x) = – 6 2x + 4x = – 6 6x = – 6 x = – 1y = – 2x y = – 2(– 1) y =
3.5 Solving Systems of Equations in Three Variables The student will be able to solve systems of linear equations in three variables algebraically.
Solving Systems of Equations Algebraically STEPS: 1.Solve for a variable in either equation. Get variable alone (x or y) 2.Substitute for this variable.
Another method for solving systems of equations is elimination
SOLVING SYSTEMS ALGEBRAICALLY SECTION 3-2. SOLVING BY SUBSTITUTION 1) 3x + 4y = 12 STEP 1 : SOLVE ONE EQUATION FOR ONE OF THE VARIABLES 2) 2x + y = 10.
3-2 Day 2 Solving Systems Algebraically: Elimination Method Objective: I can solve a system of equations using the elimination method.
Elimination Method: Solve the linear system. -8x + 3y=12 8x - 9y=12.
Chapter 3 Examples Section 5 Solving System of Equations Algebraically with 3 variables.
Solving Linear Systems by Substitution
Solve Linear Systems by Substitution January 28, 2014 Pages
Solving a System of Equations in Two Variables By Substitution Chapter 8.2.
Warm-up. Systems of Equations: Substitution Solving by Substitution 1)Solve one of the equations for a variable. 2)Substitute the expression from step.
Solve Linear Systems by Elimination February 3, 2014 Pages
3.5 Solving Linear Systems in Three Variables 10/4/13.
Algebra Review. Systems of Equations Review: Substitution Linear Combination 2 Methods to Solve:
3.2 Solve Linear Systems Algebraically Algebra II.
1.6 Solving Linear Systems in Three Variables 10/23/12.
Elimination Method - Systems. Elimination Method  With the elimination method, you create like terms that add to zero.
Solving a System of Equations by ELIMINATION. Elimination Solving systems by Elimination: 1.Line up like terms in standard form x + y = # (you may have.
Warm Up Find the solution to linear system using the substitution method. 1) 2x = 82) x = 3y - 11 x + y = 2 2x – 5y = 33 x + y = 2 2x – 5y = 33.
December 12, 2011 By the end of today: I will know how to solve systems by elimination.
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.
Today in Algebra 2 Get a calculator. Go over homework Notes: –Solving Systems of Equations using Elimination Homework.
6) x + 2y = 2 x – 4y = 14.
Warm UP: Solve the following systems of equations:
Entry Task   by.
Do Now  .
Solving Systems Of Equations Algebraically
Do Now Solve the following systems by what is stated: Substitution
3-2: Solving Systems of Equations using Substitution
Solving Systems of Equations
Solving Linear Systems Algebraically
Solve a system of linear equation in two variables
Lesson 7-4 part 3 Solving Systems by Elimination
Solving Systems Equations in Three Variables
3.5 Solving systems of equations in 3 variables
3-2: Solving Systems of Equations using Substitution
Solving Systems of Equations using Substitution
7.4 Solve Linear Systems by Multiplying First
3-2: Solving Systems of Equations using Substitution
3.2a – Solving Systems algebraically
Before: December 4, 2017 Solve each system by substitution. Steps:
College Algebra Chapter 5 Systems of Equations and Inequalities
Notes Solving a System by Elimination
Notes Solving a System by Elimination
Algebra 2 Ch.3 Notes Page 15 P Solving Systems Algebraically.
Unit 7, Lesson 1 Trigonometry / Pre-Calculus
Objectives Identify solutions of linear equations in two variables.
Solving systems using substitution
Systems of Equations Solve by Graphing.
3-2: Solving Systems of Equations using Substitution
Solve the linear system.
Warm Up Check to see if the point is a solution for the
Example 2B: Solving Linear Systems by Elimination
7.1 Solving Systems of Equations
3-2: Solving Systems of Equations using Substitution
3-2: Solving Systems of Equations using Substitution
3-2: Solving Systems of Equations using Substitution
3-2: Solving Systems of Equations using Substitution
Warm- Up: Solve by Substitution
Solve by Substitution 2x + y = 7 3x + 3y = - 3.
Solving Linear Systems by Graphing
Presentation transcript:

Algebra and Trigonometry by Cynthia Y. Young, © 2007 John Wiley and Sons. All rights reserved. Solving Systems of Equations

Algebra and Trigonometry by Cynthia Y. Young, © 2007 John Wiley and Sons. All rights reserved. Solving Systems of Equations (2,-6,3)

Algebra and Trigonometry by Cynthia Y. Young, © 2007 John Wiley and Sons. All rights reserved. What about this one?

Algebra and Trigonometry by Cynthia Y. Young, © 2007 John Wiley and Sons. All rights reserved. Solving Systems of Linear Equations with Three Variables Using Elimination and Substitution Step 1: Reduce the system to two equations in two variables using elimination. Step 2: Solve the resulting system of two equations using elimination or substitution. Step 3: Substitute the solutions in Step 2 into any of the original equations and solve for the third variable. Step 4: Check the solution in each of the three original equations.

What do equations with three variables look like?

Algebra and Trigonometry by Cynthia Y. Young, © 2007 John Wiley and Sons. All rights reserved. Your Turn! Click mouse to continue

Algebra and Trigonometry by Cynthia Y. Young, © 2007 John Wiley and Sons. All rights reserved. Your Turn! Click mouse to continue with answer Answer 1 of 3

Algebra and Trigonometry by Cynthia Y. Young, © 2007 John Wiley and Sons. All rights reserved. Your Turn! Click mouse to continue with answer Answer 2 of 3

Algebra and Trigonometry by Cynthia Y. Young, © 2007 John Wiley and Sons. All rights reserved. Your Turn! Answer 3 of 3

Algebra and Trigonometry by Cynthia Y. Young, © 2007 John Wiley and Sons. All rights reserved. HOMEWORK  P : 3, 5, 13, 15, 31, 33, 41, 47-49