रैखिक समीकरण के हल
एक रैखिक समीकरण के समाधान या हल को चर के सभी संभावित मानों के समुच्चय के रूप में परिभाषित किया जाता है जो दिए गए रैखिक समीकरण को संतुष्ट करते हैं।
रैखिक समीकरणों के हल के प्रकार
रैखिक समीकरणों के समुच्चय के 3 संभावित प्रकार के समाधान हैं और नीचे उल्लिखित हैं।
- अद्वितीय हल
- कोई हल नहीं
- अपरिमित रूप से अनेक हल
अद्वितीय हल
Example:
Thus, the unique solution of the given linear equation is x = 3.
No Solution
If the graphs of the linear equations are parallel, then the system of linear equations has no solution. In this case, there exists no point such that no lines intersect each other.
Example: Find the Solutions do the equations and?
Solution:
The equations and have no solution.
The line equations and are parallel to each other, and hence, they do not have solutions.
Infinitely Many Solutions
A linear equation in two variables has infinitely many solutions. For the system of linear equations, there exists a solution set of infinite points for which the L.H.S of an equation becomes R.H.S. The graph for the system of linear equations with infinitely many solutions is a graph of straight lines that overlaps each other.
Example: Find four different solutions of the equation
| 2 | 2 | 6 |
| 0 | 3 | 6 |
| 6 | 0 | 6 |
| 4 | 1 | 6 |
Four different solutions are
