Download presentation

Presentation is loading. Please wait.

1
**Do Now: Pass out calculators.**

Pick up an Algebra I sheet from the back – work on Mac & Tolley’s Road Trip problem.

2
Objective: To solve a system of equations using substitution.

3
**Use the substitution method**

EXAMPLE 1 Use the substitution method Solve the linear system: y = 3x + 2 Equation 1 x + 2y = 11 Equation 2 SOLUTION STEP 1 Solve for y. Equation 1 is already solved for y.

4
**Use the substitution method**

EXAMPLE 1 Use the substitution method STEP 2 Substitute 3x + 2 for y in Equation 2 and solve for x. x + 2y = 11 Write Equation 2. x + 2(3x + 2) = 11 Substitute 3x + 2 for y. 7x + 4 = 11 Simplify. 7x = 7 Subtract 4 from each side. x = 1 Divide each side by 7.

5
EXAMPLE 1 Use the substitution method STEP 3 Substitute 1 for x in the original Equation 1 to find the value of y. y = 3x + 2 = 3(1) + 2 = = 5 ANSWER The solution is (1, 5).

6
**Use the substitution method**

EXAMPLE 1 GUIDED PRACTICE Use the substitution method CHECK Substitute 1 for x and 5 for y in each of the original equations. y = 3x + 2 x + 2y = 11 5 = 3(1) + 2 ? 1 + 2 (5) = 11 ? 5 = 5 11 = 11

7
**Use the substitution method**

EXAMPLE 2 Use the substitution method Solve the linear system: x – 2y = –6 Equation 1 4x + 6y = 4 Equation 2 SOLUTION STEP 1 Solve Equation 1 for x. x – 2y = –6 Write original Equation 1. x = 2y – 6 Revised Equation 1

8
**Use the substitution method**

EXAMPLE 2 Use the substitution method STEP 2 Substitute 2y – 6 for x in Equation 2 and solve for y. 4x + 6y = 4 Write Equation 2. 4(2y – 6) + 6y = 4 Substitute 2y – 6 for x. 8y – y = 4 Distributive property 14y – 24 = 4 Simplify. 14y = 28 Add 24 to each side. y = 2 Divide each side by 14.

9
**Use the substitution method**

EXAMPLE 2 Use the substitution method STEP 3 Substitute 2 for y in the revised Equation 1 to find the value of x. x = 2y – 6 Revised Equation 1 x = 2(2) – 6 Substitute 2 for y. x = –2 Simplify. ANSWER The solution is (–2, 2).

10
**Use the substitution method**

EXAMPLE 2 GUIDED PRACTICE Use the substitution method CHECK Substitute –2 for x and 2 for y in each of the original equations. Equation 1 Equation 2 4x + 6y = 4 x – 2y = –6 –2 – 2(2) = –6 ? 4(–2) + 6 (2) = 4 ? –6 = –6 4 = 4

11
EXAMPLE 1 GUIDED PRACTICE Use the substitution method for Examples 1 and 2 Solve the linear system using the substitution method. y = 2x + 5 1. 3x + y = 10 ANSWER (1, 7)

12
EXAMPLE 2 GUIDED PRACTICE Use the substitution method for Examples 1 and 2 Solve the linear system using the substitution method. x – y = 3 2. x + 2y = –6 ANSWER (0, –3)

13
EXAMPLE 2 GUIDED PRACTICE Use the substitution method for Examples 1 and 2 Solve the linear system using the substitution method. 3x + y = –7 3. –2x + 4y = 0 ANSWER (–2, –1)

14
EXAMPLE 3 Solve a multi-step problem WEBSITES Many businesses pay website hosting companies to store and maintain the computer files that make up their websites. Internet service providers also offer website hosting. The costs for website hosting offered by a website hosting company and an Internet service provider are shown in the table. Find the number of months after which the total cost for website hosting will be the same for both companies.

15
EXAMPLE 3 Solve a multi-step problem SOLUTION STEP 1 Write a system of equations. Let y be the total cost after x months. Equation 1: Internet service provider y = x

16
**Solve a multi-step problem**

EXAMPLE 3 Solve a multi-step problem Equation 2: Website hosting company y = x The system of equations is: y = x Equation 1 y = 22.45x Equation 2

17
**Solve a multi-step problem**

EXAMPLE 3 Solve a multi-step problem STEP 2 Substitute 22.45x for y in Equation 1 and solve for x. y = x Write Equation 1. 22.45x = x Substitute 22.45x for y. 0.5x = 10 Subtract 21.95x from each side. x = 20 Divide each side by 0.5. The total cost will be the same for both companies after 20 months. ANSWER

Similar presentations

OK

Bell Ringer 2. Systems of Equations 4 A system of equations is a collection of two or more equations with a same set of unknowns A system of linear equations.

Bell Ringer 2. Systems of Equations 4 A system of equations is a collection of two or more equations with a same set of unknowns A system of linear equations.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on art of war book Ias 33 earnings per share ppt online Ppt on power system stability examples Ppt on solid dielectrics glass Ppt on media revolutions Gastric anatomy and physiology ppt on cells Download ppt on area related to circles for class 10 Ppt on viruses and antivirus-shop Ppt on acid-base titration equivalence point Ppt on nutrition in animals