9.7 Solving Systems of Equations Algebraically

Slides:

Advertisements

Similar presentations

Solve a System Algebraically

Advertisements

Solving systems of equations with 2 variables Word problems (Number Problems)

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.

SOLVING SYSTEMS USING SUBSTITUTION

3-2 Solving Systems Algebraically (p. 125) Algebra 2 Prentice Hall, 2007.

Step 1: Simplify Both Sides, if possible Distribute Combine like terms Step 2: Move the variable to one side Add or Subtract Like Term Step 3: Solve for.

Thinking Mathematically Algebra: Graphs, Functions and Linear Systems 7.3 Systems of Linear Equations In Two Variables.

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 =

Objective - To solve equations with the variable in both sides. Solve. 2x + 4 = 5x x 4 = 3x = 3x 3 7 = x -5x -3x + 4 =

Equations Reducible to Quadratic

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.

1.3 Solving with Variables on Both Sides. What We Will Learn Solve linear equations that have variables on both sides Identify special solutions.

Solving by Substitution Method or Elimination (Addition) Method

Warm-up Solve the first system of equations by the Substitution Method, then graphing.

3-2 Solving Linear Systems Algebraically Objective: CA 2.0: Students solve system of linear equations in two variables algebraically.

Linear Systems of Equations Section 3.1. What is a “system” of equations?

World 1-8 Solving by Factoring. y 2 = √36 5x = 15 Recall: it requires one equation to solve for one unknown. Traditionally we find solutions to equations.

Wednesday: Factoring Warm-up Find the factors and solutions.

The Substitution Method Objectives: To solve a system of equations by substituting for a variable.

Warm-Up 1) Determine whether (-1,7) is a solution of the system. 4 minutes 3x – y = -10 2) Solve for x where 5x + 3(2x – 1) = 5. -x + y = 8.

Holt McDougal Algebra Solving Equations with Variables on Both Sides 1-5 Solving Equations with Variables on Both Sides Holt Algebra 1 Warm Up Warm.

1.3 Solving Equations with Variables on Both Sides

Solving Systems by Elimination 5.4 NOTES, DATE ____________.

8.8 Solving Multi-Step Equations and Inequalities.

3.2 Solve Linear Systems Algebraically Algebra II.

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.

ALGEBRA 1 CHAPTER 7 LESSON 5 SOLVE SPECIAL TYPES OF LINEAR SYSTEMS.

6-2 Substitution Again Goals: Solve linear systems using substitution

EQUATION IN TWO VARIABLES:

Solving Systems Of Equations Algebraically

Systems of Equations – Solving by Substitution

1-5 Equations Goals: Solve equations with one variable

Equations with variables on both sides Whiteboard practice

2-4, 2-5 Warm Up

3-2: Solving Systems of Equations using Substitution

6-2 Solving Systems using Substitution

6-2 Solving Systems Using Substitution

Solving Linear Systems Algebraically

Solving Equations with variables on each side

3-2: Solving Systems of Equations using Substitution

Solving Systems of Equations using Substitution

Objective Solve equations in one variable that contain variable terms on both sides.

3-2: Solving Systems of Equations using Substitution

Solving Equations with Variables on Both Sides Day 2

Solving Equations with Variables on Both Sides

7.2 Solving Systems of Equations by Substitution

- Finish Unit 1 test - Solving Equations variables on both sides

Algebra 2 Ch.3 Notes Page 15 P Solving Systems Algebraically.

Equations with variables on both sides Whiteboard practice

There are infinite solutions to the system.

Warm Up #30: Solve by substitution

SECTION 2-4 : SOLVING EQUATIONS WITH THE VARIABLE ON BOTH SIDES

Objective Solve equations in one variable that contain variable terms on both sides.

6-2 Substitution Again Goals: Solve linear systems using substitution

3-2: Solving Systems of Equations using Substitution

8.3 The Addition Method Also referred to as Elimination Method.

8.2 Solving by Substitution

5.2 Substitution Try this one: x = 4y y = 5x 4x – y = 75 2x + 3y = 34

6.2 Using Substitution to Solve Systems

7.1 Solving Systems of Equations

3-2: Solving Systems of Equations using Substitution

3-2: Solving Systems of Equations using Substitution

Solving Equations with Variables on Both Sides Day 2

Solving Systems by Substitution

3-2: Solving Systems of Equations using Substitution

6-3 & 6-4 Elimination Goals: Solve systems using linear combinations.

3-2: Solving Systems of Equations using Substitution

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.

Graphing and Elimination

Presentation transcript:

9.7 Solving Systems of Equations Algebraically

Solving by Substitution When one variable is alone on one side of the equation, you can substitute for that variable in the other equation. x + y = 13 x = y + 3 (y + 3) + y = 13 x = 5 + 3 2y + 3 = 13 x = 8 -3 2y = 10 (8, 5) y = 5

3 things can happen 1.) One solution 2.) many solutions (if variables cancel out leaving you with a true equation) 3.) no solution (if variables cancel out leaving you with a false equation)

Solving by Substitution (1, 7) x + y = 8 y = 2 + 5x x + (2 + 5x)= 8 y = 2 + 5(1) 6x + 2 = 8 y = 7 -2 6x = 6 x = 1

Solving by Substitution y = x + 2 3 y = 2x - 1 y = 5 x + 2 = 2x - 1 -x 2 = x - 1 (3, 5) 3 = x

Solve by Substitution Infinitely Many Solutions

If one equation is not solved for a variable…. Then you can solve for either x or y and then substitute

Solving by Substitution (4, 1) x + y = 5 2x + 3y = 11 -y Parenthesis!!! x = 5 - y 1 2(5 – y) + 3y = 11 x = 4 10 – 2y + 3y = 11 10 + y = 11 y = 1

Solving by Substitution (5, 3) 2x + y = 13 8x + 3y = 49 8x + 3( y )= 49 13 -2x -2x y = 13 – 2x 8x + 39 - 6x = 49 2x + 39 = 49 y = 13 – 2( x ) 5 -39 2x = 10 y = 3 x = 5

The sum of two numbers is 82. One number is 12 more than the other The sum of two numbers is 82. One number is 12 more than the other. What are the numbers? Let x = the larger number and y the smaller.

The difference between two numbers is 9 The difference between two numbers is 9. Three times the larger number is six times the smaller. What are the numbers?

Solve by Substitution

Homework Page 428 (8-21) all