Every equation is different from another. Just changing a single variable, sign, or constant will always result in a new equation. You can say both equations are similar to some extent but, in reality, they are different. The question is how can we prove that a small change can change the whole course? Instead of telling you, we will show how just a small change in an equation can change everything. Imagine that you are in an exam hall and you are asked to find the factors of an equation which is
. If you draw a graph of
then it would be: 
, you wrote
hence, this will change everything. Below is the graph of
: 
The solution of a system is a pair of numbers x1, y1, such that replacing x with x1 and y with y1, both equations are verified.
Adding both equations:
Plugging the value of x in the second equation:
Properties of Linear Systems
1. If both members of an equation in a system are added or subtracted by the same expression, the resulting system is equivalent.
2.If both members of the equations of a system are multiplied or divided by a nonzero number, the resultant system is equivalent.
3. If an equation of a system is added or subtracted by another equation of the same system, the resultant system is equivalent.
4.If in a system, an equation is replaced by another equation that is obtained from adding the two equations from a system previously multiplied or divided by a nonzero number, the resultant system is equivalent.
5. If the order of the equations or the order of the unknowns changes, it is another equivalent system.
Summarise with AI:
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Hi , I m Abhishek Mittal , a passionate maths assistant professor, having experience more than 10 years with almost all top brands (Cuemath, Byjus, FIITJEE, Allen) online and offline and in-person .
Want to join Superprof , Kindly guide me.
Hi Abhishek, thanks so much for reaching out! With your experience, you’d be a fantastic fit for Superprof.
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nice work
Thank you! 😊 We’re glad you found the worksheet helpful. Keep up the great work with your studies!