1.4.3 Solution to a System of Linear equations
Chapter 1: Chapter 1 · MATHEMATICS-VOLUME 1 · EN medium
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The meaning of solution to a system of linear equations can be understood by considering the following cases : Case (i) Consider the system of linear equations x = , ... ( ) + = . ... ( ) These two equations represent a pair of straight lines in two dimensional analytical geometry (see the Fig. . ). Using ( ), we get x = + y . ... ( ) Substituting ( ) in ( ) and simplifying, we get y = . Substituting y = in ( ) and simplifying, we get x = . Both equations ( ) and ( ) are satisfied by x = and y = . That is, a solution of ( ) is also a solution of ( ) . So, we say that the system is consistent and has unique solution ( , ) . The point ( , ) is the point of intersection of the two lines and x .
📖 Class 12 Mathematics English Volume 1 2025 Edition www.tntextbooks.in · Page 37
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The meaning of solution to a system of linear equations can be understood by considering the following cases : Case (i) Consider the system of linear equations x = , ... ( ) + = . ... ( ) These two equations represent a pair of straight lines in two dimensional analytical geometry (see the Fig.
. ). Using ( ), we get x = + y . ...
( ) Substituting ( ) in ( ) and simplifying, we get y = . Substituting y = in ( ) and simplifying, we get x = . Both equations ( ) and ( ) are satisfied by x = and y = . That is, a solution of ( ) is also a solution of ( ) .
So, we say that the system is consistent and has unique solution ( , ) . The point ( , ) is the point of intersection of the two lines and x . Fig. .
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