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

Precalculus, Books A La Carte Edition Plus MyLab Math with eText -- Access Card Package (6th Edition)

6th Edition

ISBN: 9780134765471

Author: Robert F. 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

Determine whether the lines L₁ (t) = (-2,3, −1)t + (0,2,-3) and L2 p(s) = (2, −3, 1)s + (-10, 17, -8) intersect. If they do, find the point of intersection.

Convert the line given by the parametric equations y(t) Enter the symmetric equations in alphabetic order. (x(t) = -4+6t = 3-t (z(t) = 5-7t to symmetric equations.

Find the point at which the line (t) = (4, -5,-4)+t(-2, -1,5) intersects the xy plane.

Chapter 8 Solutions

Precalculus, Books A La Carte Edition Plus MyLab Math with eText -- Access Card Package (6th Edition)

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