Download presentation

Presentation is loading. Please wait.

1
**Use the substitution method**

EXAMPLE 1 Use the substitution method Solve the system using the substitution method. 2x + 5y = –5 Equation 1 x + 3y = 3 Equation 2 SOLUTION STEP 1 Solve Equation 2 for x. x = –3y + 3 Revised Equation 2

2
**Use the substitution method**

EXAMPLE 1 Use the substitution method STEP 2 Substitute the expression for x into Equation 1 and solve for y. 2x +5y = –5 Write Equation 1. 2(–3y + 3) + 5y = –5 Substitute –3y + 3 for x. y = 11 Solve for y. STEP 3 Substitute the value of y into revised Equation 2 and solve for x. x = –3y + 3 Write revised Equation 2. x = –3(11) + 3 Substitute 11 for y. x = –30 Simplify.

3
**Use the substitution method**

EXAMPLE 1 Use the substitution method The solution is (– 30, 11). ANSWER CHECK Check the solution by substituting into the original equations. 2(–30) + 5(11) –5 = ? Substitute for x and y. = ? –30 + 3(11) 3 –5 = –5 Solution checks. 3 = 3

4
**Use the elimination method**

EXAMPLE 2 Use the elimination method Solve the system using the elimination method. 3x – 7y = 10 Equation 1 6x – 8y = 8 Equation 2 SOLUTION STEP 1 Multiply Equation 1 by – 2 so that the coefficients of x differ only in sign. 3x – 7y = 10 –6x + 14y = 220 6x – 8y = 8 6x – 8y = 8

5
**Use the elimination method**

EXAMPLE 2 Use the elimination method STEP 2 Add the revised equations and solve for y. 6y = –12 y = –2 STEP 3 Substitute the value of y into one of the original equations. Solve for x. 3x – 7y = 10 Write Equation 1. 3x – 7(–2) = 10 Substitute –2 for y. 3x + 14 = 10 Simplify. x = 4 3 – Solve for x.

6
EXAMPLE 2 Use the elimination method The solution is ( , –2) 4 3 – ANSWER CHECK You can check the solution algebraically using the method shown in Example 1. You can also use a graphing calculator to check the solution.

7
GUIDED PRACTICE for Examples 1 and 2 Solve the system using the substitution or the elimination method. 1. 4x + 3y = –2 x + 5y = –9 2. 3x + 3y = –15 5x – 9y = 3 The solution is (1,–2). ANSWER The solution is ( , –2) 3 – ANSWER

8
GUIDED PRACTICE for Examples 1 and 2 Solve the system using the substitution or the elimination method. 3. 3x – 6y = 9 –4x + 7y = –16 ANSWER The solution is (11, 4)

Similar presentations

© 2022 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google