Explanation Given Information: The Linear equation system is, a 1 x + b 1 y = c 1 a 2 x + b 2 y = c 2 Proof: The solution of given system can be obtained by using the Cramer’s rule, | a 1 b 1 a 2 b 2 | = | c 1 c 2 | x = D x D and y = D y D D = | a 1 b 1 a 2 b 2 | = a 1 ⋅ b 2 − b 1 ⋅ a 2 D x = | c 1 b 1 c 2 b 2 | = c 1 ⋅ b 2 − b 1 ⋅ c 2 D y = | a 1 c 1 a 2 c 2 | = a 1 ⋅ c 2 − c 1 ⋅ a 2 So, x = c 1 ⋅ b 2 − b 1 ⋅ c 2 a 1 ⋅ b 2 − b 1 ⋅ a 2 (i) y = a 1 ⋅ c 2 − c 1 ⋅ a 2 a 1 ⋅ b 2 − b 1 ⋅ a 2 (ii) Now consider the first equation as a sum of two equation i.e. a 1 x + b 1 y = c 1 As a sum of two equation, a 3 x + b 3 y = c 3 a 4 x + b 4 y = c 4 Where, a 1 = a 3 + a 4 ( i i i ) b 1 = b 3 + b 4 ( i v ) c 1 = c 3 + c 4 ( v ) So, equation 1 can be written as, ( a 3 + a 4 ) x + ( b 3 + b 4 ) y = c 3 + c 4

6th Edition

ISBN: 8220103679510

Author: Blitzer

Publisher: PEARSON

See similar textbooks

Videos

Question

Chapter 8.5, Problem 74PE

To determine

To Prove: Use Cramer’s Rule to prove that if the first equation of the system is replaced by the sum of the two equations, the resulting system has the same solution as the original system.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 8.5, Problem 73PE

Chapter 8.5, Problem 75PE

Students have asked these similar questions

5:38 Video Message instructor Submit Question ||| D

8:38 *** TEMU TEMU -3 -2 7 B 2 1 & 5G. 61% 1 2 -1 Based on the graph above, determine the amplitude, period, midline, and equation of the function. Use f(x) as the output. Amplitude: 2 Period: 2 Midline: 2 ☑ syntax error: this is not an equation. Function: f(x) = −2 cos(πx + 2.5π) +2× Question Help: Worked Example 1 ☑ Message instructor Submit Question ||| <

8:39 *** TEMU 5G 60% A ferris wheel is 28 meters in diameter and boarded from a platform that is 2 meters above the ground. The six o'clock position on the ferris wheel is level with the loading platform. The wheel completes 1 full revolution in 4 minutes. The function h = f(t) gives your height in meters above the ground t minutes after the wheel begins to turn. What is the amplitude? 14 meters What is the equation of the Midline? y = 16 What is the period? 4 meters minutes The equation that models the height of the ferris wheel after t minutes is: f(t): = ƒ (3) = ·−14(0) + 16 syntax error: you gave an equation, not an expression. syntax error. Check your variables - you might be using an incorrect one. How high are you off of the ground after 3 minutes? Round your answe the nearest meter. ||| <

Chapter 8 Solutions

EBK PRECALCULUS

Ch. 8.1 - Check Point 1 Write the augmented matrix for the...Ch. 8.1 - Check Point 2 Use the matrix ...Ch. 8.1 - Check Point 3 Use matrices to solve the system:...Ch. 8.1 - Check Point 4 Use matrices to solve the system:...Ch. 8.1 - Check Point 5 Solve the system in Check Point. 3...Ch. 8.1 - Prob. 1CVC Ch. 8.1 - Fill in each blank so that the resulting statement...Ch. 8.1 - Prob. 3CVC Ch. 8.1 - Prob. 4CVC Ch. 8.1 - Fill in each blank so that the resulting statement...

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

To Prove: Use Cramer’s Rule to prove that if the first equation of the system is replaced by the sum of the two equations, the resulting system has the same solution as the original system.

Solution Summary: The author explains the Cramer’s Rule to prove that if the first equation of the system is replaced by the sum of two equations, the resulting system has the same solution as the original system.

Videos

To Prove: Use Cramer’s Rule to prove that if the first equation of the system is replaced by the sum of the two equations, the resulting system has the same solution as the original system.

Want to see the full answer?

Chapter 8 Solutions