To find : the solution to the given system of equation using substitution method
Answer to Problem 23E
There is NO solution to the given system of equation
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 Substitution:
1. Solve one of the equations for one variable in terms of the other.
2. Substitute the expression found in Step 1 into the other equation to obtain an equation in one variable.
3. Solve the equation obtained in Step 2.
4. Back-substitute the value obtained in Step 3 into the expression obtained in Step 1 to find the value of the other variable.
5. Check that the solution satisfies each of the original equations.
Calculation:
Description | Steps |
Label the given equation | |
Add | |
Combine like terms in both sides |
Calculation (Continued):
Description | Steps |
Multiply -1 throughout the equation | |
Substitute | |
Distribute 6 in left side of the equation | |
Simplify fraction in left side of the equation | |
Combine like terms in left side of the equation |
Conclusion:
Since we end up with an equation that is not true, there is no solution to the given system of equation, if drawn the two lines will never meet and will be parallel to each other.
Chapter 7 Solutions
EBK PRECALCULUS W/LIMITS
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning