Download presentation

Presentation is loading. Please wait.

Published byMichael Cross Modified over 5 years ago

1
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 substitution: 11x – 7y = - 14 x – 2y = -4

2
Objective: To solve systems of equations using elimination (adding or subtracting).

3
Use addition to eliminate a variable EXAMPLE 1 Solve the linear system: 2x + 3y = 11 –2x + 5y = 13 Equation 1 Equation 2 SOLUTION Add the equations to eliminate one variable. 2x + 3y = 11 –2x + 5y = 13 Solve for y. 8y = 24 y = 3 STEP 1 STEP 2

4
Use addition to eliminate a variable EXAMPLE 1 2x + 3y = 11 Write Equation 1 2x + 3(3) = 11 Substitute 3 for y. x = 1 Solve for x. ANSWER The solution is (1, 3). Substitute 3 for y in either equation and solve for x. STEP 3

5
Use addition to eliminate a variable EXAMPLE 1 2x + 3y = 11 11 = 11 Substitute 1 for x and 3 for y in each of the original equations. CHECK 2(1) + 3(3) = 11 ? 2x + 5y = 13 13 = 13 2(1) + 5(3) = 13 ?

6
Use subtraction to eliminate a variable EXAMPLE 2 Solve the linear system: 4x + 3y = 2 Equation 1 5x + 3y = –2 Equation 2 SOLUTION Subtract the equations to eliminate one variable. 4x + 3y = 2 5x + 3y = –2 Solve for x. – x = 4 STEP 1 STEP 2 x = 4

7
Use subtraction to eliminate a variable EXAMPLE 2 4x + 3y = 2 Write Equation 1. 4(–4) + 3y = 2 Substitute –4 for x. y = 6 Solve for y. ANSWER The solution is (–4, 6). Substitute 4 for x in either equation and solve for y. STEP 3

8
Arrange like terms EXAMPLE 3 Solve the linear system: 8x – 4y = –4 Equation 1 4y = 3x + 14 Equation 2 SOLUTION STEP 1 Rewrite Equation 2 so that the like terms are arranged in columns. 8x – 4y = –4 4y = 3x + 14 8x – 4y = –4 3x + 4y = 14 STEP 2 Add the equations. 5x = 10 STEP 3 Solve for x. x = 2

9
Arrange like terms EXAMPLE 3 4y = 3x + 14 Write Equation 2. 4y = 3(2) + 14 Substitute 2 for x. y = 5 Solve for y. ANSWER The solution is (2, 5). STEP 4 Substitute 2 for x in either equation and solve for y.

10
GUIDED PRACTICE for Example 1,2 and 3 Solve the linear system: 4x – 3y = 5 –2x + 3y = –7 ` 1. ANSWER (–1, –3)

11
GUIDED PRACTICE for Example 1,2 and 3 Solve the linear system: 5x + 2y = 4 5x – 6y = 8– 2. ANSWER (2, –3)

12
GUIDED PRACTICE for Example 1,2 and 3 Solve the linear system: 6x – 4y = 14 3x + 4y = 1 – 3. ANSWER (5, 4)

13
GUIDED PRACTICE for Example 1,2 and 3 Solve the linear system: 7x – 2y = 5 7x – 3y = 4 4. ANSWER (1, 1)

14
GUIDED PRACTICE for Example 1,2 and 3 Solve the linear system: 3x + 4y = –6 5. = 3x + 6 2y2y ANSWER (–2, 0)

15
GUIDED PRACTICE for Example 1,2 and 3 Solve the linear system: 2x + 5y = 12 6. = 4x + 6 5y5y ANSWER (1, 2)

Similar presentations

© 2021 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