Maths is something that is both interesting and complicated. Whether you are a lover of this subject or you don’t like it, in both the scenarios, you have to understand the concepts so as to get the exact meaning of concepts. Of course, maths is not at all a child’s play unless you know its deep rooted concepts.
Whether you have doubts in triangles, want to understand something regarding NCERT Solutions for Class 9 Linear Equations in Two Variables or have any other issues related to maths, you can clarify them with the right set of solutions and correct assistance.
Talking about Linear Equations, first of all, you have to understand the System of Linear Equations. A system of linear equations is 2 or more linear equations that are getting solved simultaneously. Here it is important that you know the Solution of a system. In usual, a solution of system in two variables is the ordered pair that makes BOTH the equations true. In simple words, it is wherein the two graphs cross, what they possess in common. So in case an ordered pair is solution to an equation, but not the other one, then it is NOT at all a solution to a system. After all, a consistent system is a system that possesses at least a solution. And an inconsistent system is the system that possesses no solution. The equations of a system are reliant on in case ALL the solutions of an equation are also the solutions of the other equation. In simple words, they end up being same line. The equations of a system are independent in case they do not share ALL the solutions. They can possess one point in common, not all of them.
There are three likely outcomes that you might encounter when working on these systems:
- one solution
- No solution
- infinite solutions
In case the system in two variables possesses one solution, it will be an ordered pair that is a solution to BOTH the equations. In simple words, when one plugs in the values of ordered pair it makes BOTH the equations TRUE. In case you do get one solution for the final answer, is this system consistent or inconsistent? If you have just said consistent, just give yourself a pat on your back. In case you have said independent, you are right!
In case there are two lines that are parallel to each other, they shall never intersect. It simply means they won’t have any points in common. In such a situation, you shall have no solution. In case you get no solution for the final answer, is this system consistent or inconsistent? If you have said inconsistent, you are absolutely right!
The Infinite Solutions
In case two lines end up lying on the top of each other, then there will be an infinite number of solutions. In such a situation, they would end up in the same line, so any type of solution that work in an equation is going to work in other.
Thus, if you are still perplexed about linear concepts or want to know something else like cbse class 9 Maths chapters 4, just explore platforms catering easy and finest solutions for your issues.