What is meant by a solution to a system of linear equations?
The meaning of the solution to a system of linear equations.
Answer to Problem 1FCCE
Solution:
A solution to the system of linear equations is the point of intersection of line or plane corresponding to equations in the system or is the value of the variables takes as x, y, z.
Explanation of Solution
A system of linear equations represents line or plane and the point where they intersect is the solution of the system as that point satisfies all the equations in the system.
That is, the intersection is the value of the variables.
For example:
Consider a system of linear equations,
On solving the above equation as:
And,
Put
So,
This system represents two lines and they intersect at point
Therefore, the solution of the system of linear equation is the value of the variables.
Want to see more full solutions like this?
Chapter 2 Solutions
Finite Mathematics & Its Applications (12th Edition)
Additional Math Textbook Solutions
Pathways to Math Literacy (Loose Leaf)
A Problem Solving Approach To Mathematics For Elementary School Teachers (13th Edition)
Mathematics for Elementary Teachers with Activities (5th Edition)
Excursions in Modern Mathematics (9th Edition)
Mathematical Ideas (13th Edition) - Standalone book
- Can a system of linear equations have exactly two solutions? Explain why or why not.arrow_forwardHow can you tell when a system of three linear equations with three variables has no solution? Infinitely many solutions?arrow_forwardIn a system of linear equations, the two equations have the same slope. Describe the possible solutions to the system.arrow_forward
- Can a linear system of three equations have exactly two solutions? Explain why or why notarrow_forwardIn a system of linear equations, the two equations have the same intercepts. Describe the possible solutions to the system.arrow_forwardCan you explain whether there can be only one method to solve a linear system of equations? If yes, give an example of such a system of equations. If not, explain why not.arrow_forward
- Write a uniform motion problem similar to Example 4.15 that relates to where you live with your friends or family members. Then translate to a system of equations and solve it.arrow_forwardFor a system of two linear equations in two variables, aHow many solutions are possible? bWhat is meant by an inconsistent system? cWhat is meant by a dependent system?arrow_forwardUsing the method of addition, is there only one way to solve the system?arrow_forward
- In Exercises 1-6, determine which equations are linear equations in the variables x, y, and z. If any equation is not linear, explain why not. 4.arrow_forwardExplain in your own words how to solve a system of equations using substitution.arrow_forwardWrite an application problem similar to Example 4.14. Then translate to a system of equations and solve it.arrow_forward
- Holt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGALBig Ideas Math A Bridge To Success Algebra 1: Stu...AlgebraISBN:9781680331141Author:HOUGHTON MIFFLIN HARCOURTPublisher:Houghton Mifflin HarcourtGlencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill
- Algebra: Structure And Method, Book 1AlgebraISBN:9780395977224Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. ColePublisher:McDougal LittellCollege Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage Learning