EBK PRECALCULUS W/LIMITS
4th Edition
ISBN: 9781337516853
Author: Larson
Publisher: CENGAGE CO
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Question
Chapter 7.3, Problem 31E
To determine
To find : the solution to the given system of linear equations
Expert Solution & Answer
Answer to Problem 31E
The solution to the given system of equation is
Explanation of Solution
Given information : The system of equation is
Concept Involved:
Solution of a system of equation is the point which makes both the equation TRUE.
Graphically the solution to the system of equation is the point where the two lines meet.
Method of Elimination:
To use the method of elimination to solve a system of two linear equations in x and y, perform the following steps.
1. Obtain coefficients for x (or y) that differ only in sign by multiplying all
terms of one or both equations by suitably chosen constants.
2. Add the equations to eliminate one variable.
3. Solve the equation obtained in Step 2.
4. Back-substitute the value obtained in Step 3 into either of the original
equations and solve for the other variable.
5. Check that the solution satisfies each of the original equations.
The Number of Solutions of a Linear System
For a system of linear equations, exactly one of the following is true.
1. There is exactly one solution.
2. There are infinitely many solutions.
3. There is no solution.
Calculation:
| Description | Steps | |
| Label the given equations | ▶ 1st equation | |
| ▶ 2nd equation | ||
| ▶ 3rd equation | ||
| In order to eliminate y, multiply -1 to the 1stequation and add the result to the 3rdequation | ||
| Label the new equation as 4th equation | ▶ 4th equation | |
| In order to eliminate the same y variable, multiply -1 with the 1st equation and add the result to the 3rd equation | ||
| Label the new equation as 5th equation | ▶ 5th equation | |
| In order to eliminate the variable z , multiply 3 to the 4th equation and add the result to the 5th equation | ||
| Solve the equation | ||
| Substitute By dividing -1 on both sides | ||
| Substitute | ||
Calculation (Continued):
| Description | Steps |
| Checking the solution | |
| Checking the solution | |
| Checking the solution |
Conclusion:
The solution to the given system of equation is
Chapter 7 Solutions
EBK PRECALCULUS W/LIMITS
Ch. 7.1 - Prob. 1ECh. 7.1 - Prob. 2ECh. 7.1 - Prob. 3ECh. 7.1 - Prob. 4ECh. 7.1 - Prob. 5ECh. 7.1 - Prob. 6ECh. 7.1 - Prob. 7ECh. 7.1 - Prob. 8ECh. 7.1 - Prob. 9ECh. 7.1 - Prob. 10E
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