Download presentation

Presentation is loading. Please wait.

Published byEverett Burrell Modified over 2 years ago

1
EXAMPLE 3 Use Cramer’s rule for a 2 X 2 system Use Cramer’s rule to solve this system: 3x 5y = 21 9x + 4y = 6 – SOLUTION STEP 1 Evaluate the determinant of the coefficient matrix. 9 4 3 –5 = –45 – 12 = –57

2
EXAMPLE 3 Use Cramer’s rule for a 2 X 2 system STEP 2 Apply Cramer’s rule because the determinant is not 0. x = –6 4 –21 –5 –57 = –57 30 – (–84) = –57 114 = –2 y = 9 –6 3 –21 –57 = –57 –189 – (–18) = –57 –171 3 ANSWER The solution is ( 2, 3). –

3
**Use Cramer’s rule for a 2 X 2 system**

EXAMPLE 3 Use Cramer’s rule for a 2 X 2 system CHECK Check this solution in the original equations. 9x + 4y = –6 3x – 5y = –21 9(–2) + 4(3) = –6 ? ? 3(–2) – 5(3) = –21 – = –6 ? –6 – 15 = –21 ? –6 = –21 = –21

4
EXAMPLE 4 Solve a multi-step problem CHEMISTRY The atomic weights of three compounds are shown. Use a linear system and Cramer’s rule to find the atomic weights of carbon (C), hydrogen (H), and oxygen (O).

5
EXAMPLE 4 Solve a multi-step problem SOLUTION STEP 1 Write a linear system using the formula for each compound. Let C, H, and O represent the atomic weights of carbon, hydrogen, and oxygen. 6C + 12H + 6O = 180 C O = 44 2H + 2O = 34

6
EXAMPLE 4 Solve a multi-step problem STEP 2 Evaluate the determinant of the coefficient matrix. 6 1 12 2 = ( ) ( ) = 36 – STEP 3 Apply Cramer’s rule because the determinant is not 0. 180 34 12 6 2 1 44 C = H = O = 36 –

7
EXAMPLE 4 Solve a multi-step problem 576 36 – = 432 = = = ANSWER The atomic weights of carbon, hydrogen, and oxygen are 12, 1, and 16, respectively.

8
GUIDED PRACTICE for Examples 3 and 4 Use Cramer’s rule to solve the linear system. 5. 3x – 4y = –15 6. 4x + 7y = 2 –3x – 2y = 28 7. 3x – 4y + 2z = 18 2x + 5y = 13 4x + y – 5z = –13 2x – 3y + z = 11 (–1, 3). ANSWER (4, –2). ANSWER (2, –1, 4). ANSWER

Similar presentations

OK

Section 3.5 Solving Systems of Linear Equations in Two Variables by the Addition Method.

Section 3.5 Solving Systems of Linear Equations in Two Variables by the Addition Method.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on cryogenic engine Ppt on uninterrupted power supply Ppt on bluetooth based smart sensor networks Ppt on chapter management of natural resources Ppt on review writing lesson Ppt on kirchhoff's current and voltage laws Ppt on famous indian entrepreneurship Ppt on save environment in hindi Ppt on viruses and bacteria Ppt on fibonacci series