Use an inverse matrix to solve each system of linear equations. (a) x+ 2y - 1 x- 2y - -3 (X, y) = (b) x+ 2y = 11 X- 2y - -5 x, y)%3D
Use an inverse matrix to solve each system of linear equations. (a) x+ 2y - 1 x- 2y - -3 (X, y) = (b) x+ 2y = 11 X- 2y - -5 x, y)%3D
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![**Solving Systems of Linear Equations Using Inverse Matrix**
Given below are two systems of linear equations. Use an inverse matrix to find the solution for each system.
**(a)**
1. \( x + 2y = 1 \)
2. \( x - 2y = -3 \)
Find \((x, y)\):
\[ (x, y) = \boxed{\phantom{insert\ solution\ here}} \]
**(b)**
1. \( x + 2y = 11 \)
2. \( x - 2y = -5 \)
Find \((x, y)\):
\[ (x, y) = \boxed{\phantom{insert\ solution\ here}} \]
---
In both cases, express the system of equations in matrix form and use the inverse of the coefficient matrix to solve for the variables \(x\) and \(y\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F350a872a-0bb3-4218-bc06-9a68f5ae92af%2F1407e00a-07b3-49ce-a50b-2ea959f23f94%2Fc3t760b_processed.png&w=3840&q=75)
Transcribed Image Text:**Solving Systems of Linear Equations Using Inverse Matrix**
Given below are two systems of linear equations. Use an inverse matrix to find the solution for each system.
**(a)**
1. \( x + 2y = 1 \)
2. \( x - 2y = -3 \)
Find \((x, y)\):
\[ (x, y) = \boxed{\phantom{insert\ solution\ here}} \]
**(b)**
1. \( x + 2y = 11 \)
2. \( x - 2y = -5 \)
Find \((x, y)\):
\[ (x, y) = \boxed{\phantom{insert\ solution\ here}} \]
---
In both cases, express the system of equations in matrix form and use the inverse of the coefficient matrix to solve for the variables \(x\) and \(y\).
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