Presentation is loading. Please wait.

Presentation is loading. Please wait.

Honors Algebra II 3.5 Solving Systems with Three Variables.

Published byBlaze Hart Modified over 6 years ago

Similar presentations

Presentation on theme: "Honors Algebra II 3.5 Solving Systems with Three Variables."— Presentation transcript:

1 Honors Algebra II 3.5 Solving Systems with Three Variables.

2 Solving Systems of Equations in 3 variables by Elimination: Example 1: Solve the system by elimination. (Number the equations to make it easier!) GOAL: Eliminate one of the variables at a time.

3 Solving Systems of Equations in 3 variables by Elimination: Example 1: Solve the system by elimination. (Number the equations to make it easier!) GOAL: Eliminate one of the variables at a time. Equation #1 Equation #2 Equation #3

4 Solving Systems of Equations in 3 variables by Elimination: Example 1: Solve the system by elimination. (Number the equations to make it easier!) GOAL: Eliminate one of the variables at a time. Equation #1 Equation #2 Equation #3 Equation #1 and #2 have the opposite coefficients for y, so that term can be easily eliminated.

5 Solving Systems of Equations in 3 variables by Elimination: Example 1: Solve the system by elimination. (Number the equations to make it easier!) GOAL: Eliminate one of the variables at a time. Equation #1 Equation #2 Equation #3 Equation #1 and #2 have the opposite coefficients for y, so that term can be easily eliminated. ZAP THE y-TERMS!!!

6 Solving Systems of Equations in 3 variables by Elimination: Example 1: Solve the system by elimination. (Number the equations to make it easier!) GOAL: Eliminate one of the variables at a time. Equation #1 Equation #2 Equation #3 Equation #1 and #2 have the opposite coefficients for y, so that term can be easily eliminated. ZAP THE y-TERMS!!! Equation #1 + Equation #2

7 Solving Systems of Equations in 3 variables by Elimination: Example 1: Solve the system by elimination. (Number the equations to make it easier!) GOAL: Eliminate one of the variables at a time. Equation #1 Equation #2 Equation #3 Equation #1 and #2 have the opposite coefficients for y, so that term can be easily eliminated. ZAP THE y-TERMS!!! Equation #1 + Equation #2

8 Solving Systems of Equations in 3 variables by Elimination: Example 1: Solve the system by elimination. (Number the equations to make it easier!) GOAL: Eliminate one of the variables at a time. Equation #1 Equation #2 Equation #3 Equation #2 and #3 have the opposite coefficients for y, so that term can be easily eliminated. Equation #1 + Equation #2 Equation #2 + Equation #3

9 Solving Systems of Equations in 3 variables by Elimination: Example 1: Solve the system by elimination. (Number the equations to make it easier!) GOAL: Eliminate one of the variables at a time. Equation #1 Equation #2 Equation #3 Equation #2 and #3 have the opposite coefficients for y, so that term can be easily eliminated. ZAP THE y-TERMS!!! Equation #1 + Equation #2 Equation #2 + Equation #3

10 Solving Systems of Equations in 3 variables by Elimination: Example 1: Solve the system by elimination. (Number the equations to make it easier!) GOAL: Eliminate one of the variables at a time. Equation #1 Equation #2 Equation #3 Equation #2 and #3 have the opposite coefficients for y, so that term can be easily eliminated. Equation #1 + Equation #2 Equation #2 + Equation #3

11 Solving Systems of Equations in 3 variables by Elimination: Example 1: Solve the system by elimination. (Number the equations to make it easier!) GOAL: Eliminate one of the variables at a time. Equation #1 Equation #2 Equation #3 Equation #2 and #3 have the opposite coefficients for y, so that term can be easily eliminated. Equation #1 + Equation #2 Equation #2 + Equation #3

12 Solving Systems of Equations in 3 variables by Elimination: Example 1: Solve the system by elimination. (Number the equations to make it easier!) GOAL: Eliminate one of the variables at a time. Equation #1 Equation #2 Equation #3 Equation #2 and #3 have the opposite coefficients for y, so that term can be easily eliminated. Equation #1 + Equation #2 Equation #2 + Equation #3 Now we have two equations with two variables… just like we’ve been doing!

13 Solving Systems of Equations in 3 variables by Elimination: Example 1: Solve the system by elimination. (Number the equations to make it easier!) GOAL: Eliminate one of the variables at a time. Equation #1 Equation #2 Equation #3 Equation #1 + #2 Equation #2 + #3

14 Solving Systems of Equations in 3 variables by Elimination: Example 1: Solve the system by elimination. (Number the equations to make it easier!) GOAL: Eliminate one of the variables at a time. Equation #1 Equation #2 Equation #3 Equation #1 + #2 Equation #2 + #3 The z-values are opposites, so add straight down to eliminate the z-terms. ZAP THE z-TERMS!!!

15 Solving Systems of Equations in 3 variables by Elimination: Example 1: Solve the system by elimination. (Number the equations to make it easier!) GOAL: Eliminate one of the variables at a time. Equation #1 Equation #2 Equation #3 Equation #1 + #2 Equation #2 + #3 The z-values are opposites, so add straight down to eliminate the z-terms. ZAP THE z-TERMS!!!

16 Solving Systems of Equations in 3 variables by Elimination: Example 1: Solve the system by elimination. (Number the equations to make it easier!) GOAL: Eliminate one of the variables at a time. Equation #1 Equation #2 Equation #3 Equation #1 + #2 Equation #2 + #3 The z-values are opposites, so add straight down to eliminate the z-terms. ZAP THE z-TERMS!!!

17 We now have one of the three values. Just two more to go!!!
Solving Systems of Equations in 3 variables by Elimination: Example 1: Solve the system by elimination. (Number the equations to make it easier!) GOAL: Eliminate one of the variables at a time. Equation #1 Equation #2 Equation #3 Equation #1 + #2 Equation #2 + #3 The z-values are opposites, so add straight down to eliminate the z-terms. ZAP THE z-TERMS!!! We now have one of the three values. Just two more to go!!!

18 Solving Systems of Equations in 3 variables by Elimination: Example 1: Solve the system by elimination. (Number the equations to make it easier!) GOAL: Eliminate one of the variables at a time. Equation #1 Equation #2 Equation #3 Equation #1 + #2 Equation #2 + #3

19 Solving Systems of Equations in 3 variables by Elimination: Example 1: Solve the system by elimination. (Number the equations to make it easier!) GOAL: Eliminate one of the variables at a time. Equation #1 Equation #2 Equation #3 Equation #1 + #2 Equation #2 + #3 Plug the value for x back into one of the equations and solve for z.

20 Solving Systems of Equations in 3 variables by Elimination: Example 1: Solve the system by elimination. (Number the equations to make it easier!) GOAL: Eliminate one of the variables at a time. Equation #1 Equation #2 Equation #3 Equation #1 + #2 Equation #2 + #3 Plug the value for x back into one of the equations and solve for z.

21 Solving Systems of Equations in 3 variables by Elimination: Example 1: Solve the system by elimination. (Number the equations to make it easier!) GOAL: Eliminate one of the variables at a time. Equation #1 Equation #2 Equation #3 Equation #1 + #2 Equation #2 + #3 Plug the value for x back into one of the equations and solve for z.

22 We now have TWO of the three values. Just ONE more to go!!!
Solving Systems of Equations in 3 variables by Elimination: Example 1: Solve the system by elimination. (Number the equations to make it easier!) GOAL: Eliminate one of the variables at a time. Equation #1 Equation #2 Equation #3 Equation #1 + #2 Equation #2 + #3 Plug the value for x back into one of the equations and solve for z. We now have TWO of the three values. Just ONE more to go!!!

23 Solving Systems of Equations in 3 variables by Elimination: Example 1: Solve the system by elimination. (Number the equations to make it easier!) GOAL: Eliminate one of the variables at a time. Equation #1 Equation #2 Equation #3 Plug both values back into one of the original equations and solve for the final value, y.

24 Solving Systems of Equations in 3 variables by Elimination: Example 1: Solve the system by elimination. (Number the equations to make it easier!) GOAL: Eliminate one of the variables at a time. Equation #1 Equation #2 Equation #3 Plug both values back into one of the original equations and solve for the final value, y.

25 Solving Systems of Equations in 3 variables by Elimination: Example 1: Solve the system by elimination. (Number the equations to make it easier!) GOAL: Eliminate one of the variables at a time. Equation #1 Equation #2 Equation #3 Plug both values back into one of the original equations and solve for the final value, y.

26 Solving Systems of Equations in 3 variables by Elimination: Example 1: Solve the system by elimination. (Number the equations to make it easier!) GOAL: Eliminate one of the variables at a time. Equation #1 Equation #2 Equation #3 Plug both values back into one of the original equations and solve for the final value, y.

27 Solving Systems of Equations in 3 variables by Elimination: Example 1: Solve the system by elimination. (Number the equations to make it easier!) GOAL: Eliminate one of the variables at a time. Equation #1 Equation #2 Equation #3 Plug both values back into one of the original equations and solve for the final value, y.

28 Solving Systems of Equations in 3 variables by Elimination: Example 1: Solve the system by elimination. (Number the equations to make it easier!) GOAL: Eliminate one of the variables at a time. Equation #1 Equation #2 Equation #3 Plug both values back into one of the original equations and solve for the final value, y.

29 We’ve found all three values!!!
Solving Systems of Equations in 3 variables by Elimination: Example 1: Solve the system by elimination. (Number the equations to make it easier!) GOAL: Eliminate one of the variables at a time. Equation #1 Equation #2 Equation #3 WOO HOO!!! We’re done! We’ve found all three values!!! Our answer is (5, 1, -2)

30 Solving Systems of Equations in 3 variables by Elimination: Example 1: Solve the system by elimination. (Number the equations to make it easier!) GOAL: Eliminate one of the variables at a time.

31 Solving Systems of Equations in 3 variables by Elimination: Example 1: Solve the system by elimination. (Number the equations to make it easier!) GOAL: Eliminate one of the variables at a time. Equation #1 Equation #2 Equation #3

32 Solving Systems of Equations in 3 variables by Elimination: Example 1: Solve the system by elimination. (Number the equations to make it easier!) GOAL: Eliminate one of the variables at a time. ZAP THE y-TERMS!!! Equation #1 Equation #2 Equation #3

33 Solving Systems of Equations in 3 variables by Elimination: Example 1: Solve the system by elimination. (Number the equations to make it easier!) GOAL: Eliminate one of the variables at a time. ZAP THE y-TERMS!!! Equation #1 Equation #2 Equation #3 Equation #1 +Equation #2

34 Solving Systems of Equations in 3 variables by Elimination: Example 1: Solve the system by elimination. (Number the equations to make it easier!) GOAL: Eliminate one of the variables at a time. ZAP THE y-TERMS!!! Equation #1 Equation #2 Equation #3 Equation #1 +Equation #2

35 Solving Systems of Equations in 3 variables by Elimination: Example 1: Solve the system by elimination. (Number the equations to make it easier!) GOAL: Eliminate one of the variables at a time. ZAP THE y-TERMS!!! Equation #1 Equation #2 Equation #3 Equation #1 +Equation #2 Equation #1 +Equation #3

36 Solving Systems of Equations in 3 variables by Elimination: Example 1: Solve the system by elimination. (Number the equations to make it easier!) GOAL: Eliminate one of the variables at a time. ZAP THE y-TERMS!!! Equation #1 Equation #2 Equation #3 Equation #1 +Equation #2 Equation #1 +Equation #3

37 Solving Systems of Equations in 3 variables by Elimination: Example 1: Solve the system by elimination. (Number the equations to make it easier!) GOAL: Eliminate one of the variables at a time. ZAP THE y-TERMS!!! Equation #1 Equation #2 Equation #3 Equation #1 +Equation #2 Equation #1 +Equation #3

38 Solving Systems of Equations in 3 variables by Elimination: Example 1: Solve the system by elimination. (Number the equations to make it easier!) GOAL: Eliminate one of the variables at a time. Equation #1 Equation #2 Equation #3 Equation #1 + #2 Equation #1 + #3

39 Solving Systems of Equations in 3 variables by Elimination: Example 1: Solve the system by elimination. (Number the equations to make it easier!) GOAL: Eliminate one of the variables at a time. Equation #1 Equation #2 Equation #3 ZAP THE z-TERMS!!! Equation #1 + #2 Equation #1 + #3

40 Solving Systems of Equations in 3 variables by Elimination: Example 1: Solve the system by elimination. (Number the equations to make it easier!) GOAL: Eliminate one of the variables at a time. Equation #1 Equation #2 Equation #3 ZAP THE z-TERMS!!! Equation #1 + #2 Equation #1 + #3

41 Solving Systems of Equations in 3 variables by Elimination: Example 1: Solve the system by elimination. (Number the equations to make it easier!) GOAL: Eliminate one of the variables at a time. Equation #1 Equation #2 Equation #3 Equation #1 + #2 Equation #1 + #3 One down, two to go! We have our first value, x = 1.

42 Solving Systems of Equations in 3 variables by Elimination: Example 1: Solve the system by elimination. (Number the equations to make it easier!) GOAL: Eliminate one of the variables at a time. Equation #1 Equation #2 Equation #3 Equation #1 + #2 Equation #1 + #3

43 Solving Systems of Equations in 3 variables by Elimination: Example 1: Solve the system by elimination. (Number the equations to make it easier!) GOAL: Eliminate one of the variables at a time. Equation #1 Equation #2 Equation #3 Equation #1 + #2 Equation #1 + #3

44 Solving Systems of Equations in 3 variables by Elimination: Example 1: Solve the system by elimination. (Number the equations to make it easier!) GOAL: Eliminate one of the variables at a time. Equation #1 Equation #2 Equation #3 Equation #1 + #2 Equation #1 + #3

45 Solving Systems of Equations in 3 variables by Elimination: Example 1: Solve the system by elimination. (Number the equations to make it easier!) GOAL: Eliminate one of the variables at a time. Equation #1 Equation #2 Equation #3 Two down! We’re almost there!

46 Solving Systems of Equations in 3 variables by Elimination: Example 1: Solve the system by elimination. (Number the equations to make it easier!) GOAL: Eliminate one of the variables at a time. Equation #1 Equation #2 Equation #3

47 Solving Systems of Equations in 3 variables by Elimination: Example 1: Solve the system by elimination. (Number the equations to make it easier!) GOAL: Eliminate one of the variables at a time. Equation #1 Equation #2 Equation #3

48 Solving Systems of Equations in 3 variables by Elimination: Example 1: Solve the system by elimination. (Number the equations to make it easier!) GOAL: Eliminate one of the variables at a time. Equation #1 Equation #2 Equation #3

49 Solving Systems of Equations in 3 variables by Elimination: Example 1: Solve the system by elimination. (Number the equations to make it easier!) GOAL: Eliminate one of the variables at a time. Equation #1 Equation #2 Equation #3 Woo Hoo! We’re Done! (1, 2, -1)

50 Solving Systems of Equations in 3 variables by Elimination: Example 1: Solve the system by elimination. (Number the equations to make it easier!) GOAL: Eliminate one of the variables at a time.

51 Solving Systems of Equations in 3 variables by Elimination: Example 1: Solve the system by elimination. (Number the equations to make it easier!) GOAL: Eliminate one of the variables at a time. The solution is (-2, 6, -3)

52 Solving Systems of Equations in 3 variables by Elimination: Example 1: Solve the system by elimination. (Number the equations to make it easier!) GOAL: Eliminate one of the variables at a time.

53 Solving Systems of Equations in 3 variables by Elimination: Example 1: Solve the system by elimination. (Number the equations to make it easier!) GOAL: Eliminate one of the variables at a time. The solution is (2, -1, 1)

54 Solving Systems of Equations in 3 variables by Substitution: GOAL: Substitute for one of the variables to create a system with 2 variables!!!

55 Solving Systems of Equations in 3 variables by Substitution: Example 3: Solve the system by substitution. (Number the equations to make it easier!) GOAL: Substitute for one of the variables to create a system with 2 variables!!! The solution is (2, 1, -4)

56 Solving Systems of Equations in 3 variables by Substitution: Example 3: Solve the system by substitution. (Number the equations to make it easier!) GOAL: Substitute for one of the variables to create a system with 2 variables!!!

57 Solving Systems of Equations in 3 variables by Substitution: Example 3: Solve the system by substitution. (Number the equations to make it easier!) GOAL: Substitute for one of the variables to create a system with 2 variables!!! The solution is (4, 1, 5)

Download ppt "Honors Algebra II 3.5 Solving Systems with Three Variables."

Similar presentations

4.3 Systems of Equations - Elimination Objective: The student will be able to: Solve systems of equations using elimination with addition and subtraction.

4.3 Systems of Equations - Elimination Objective: The student will be able to: Solve systems of equations using elimination with addition and subtraction.
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.

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.
Drill Solve the linear system by substitution. 1.y = 6x – 11 -2x – 3y = -7 2.-4x + y = 6 -5x – y = 21.

Drill Solve the linear system by substitution. 1.y = 6x – 11 -2x – 3y = x + y = 6 -5x – y = 21.
3.5 Solving systems of equations in 3 variables

3.5 Solving systems of equations in 3 variables
Bell Work2/12/15 Solve the system by elimination..

Bell Work2/12/15 Solve the system by elimination..
Solving Systems of Equations: Elimination Method.

Solving Systems of Equations: Elimination Method.
Solving Linear Equations

Solving Linear Equations
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 =

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 =
Dr. Fowler CCM Solving Systems of Equations By Elimination – Easier.

Dr. Fowler CCM Solving Systems of Equations By Elimination – Easier.
Solve Systems of Linear Equations Using Elimination Honors Math – Grade 8.

Solve Systems of Linear Equations Using Elimination Honors Math – Grade 8.
Solving a System of Equations in Two Variables By Elimination Chapter 8.3.

Solving a System of Equations in Two Variables By Elimination Chapter 8.3.
Solving Systems of Equations. Solve systems of equations using addition and subtraction.

Solving Systems of Equations. Solve systems of equations using addition and subtraction.
Another method for solving systems of equations is elimination

Another method for solving systems of equations is elimination
Do Now A vendor sold 200 tickets for an upcoming rock concert. Floor seats were $36 and stadium seats were $28. The vendor sold $6080 in tickets. How many.

Do Now A vendor sold 200 tickets for an upcoming rock concert. Floor seats were $36 and stadium seats were $28. The vendor sold $6080 in tickets. How many.
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.

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.
Solving Systems of Equations using Elimination. Solving a system of equations by elimination using multiplication. Step 1: Put the equations in Standard.

Solving Systems of Equations using Elimination. Solving a system of equations by elimination using multiplication. Step 1: Put the equations in Standard.
Solving Systems of Equations by Elimination (Addition) Section 3.2, Part II.

Solving Systems of Equations by Elimination (Addition) Section 3.2, Part II.
Solving by Elimination Example 1: STEP 2: Look for opposite terms. STEP 1: Write both equations in Standard Form to line up like variables. STEP 5: Solve.

Solving by Elimination Example 1: STEP 2: Look for opposite terms. STEP 1: Write both equations in Standard Form to line up like variables. STEP 5: Solve.
3-2 Day 2 Solving Systems Algebraically: Elimination Method Objective: I can solve a system of equations using the elimination method.

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.

Elimination Method: Solve the linear system. -8x + 3y=12 8x - 9y=12.

Similar presentations

Ads by Google