Math, asked by Nishantanchan4352, 1 year ago

Why in a set on linear equations addition of multiple of one equation to other does not change solution?

Answers

Answered by Riyaz786
2
In mathematics, a system of linear equations(or linear system) is a collection of two or more linear equations involving the same set of variables.[1] For example,

{\displaystyle {\begin{alignedat}{7}3x&&\;+\;&&2y&&\;-\;&&z&&\;=\;&&1&\\2x&&\;-\;&&2y&&\;+\;&&4z&&\;=\;&&-2&\\-x&&\;+\;&&{\tfrac {1}{2}}y&&\;-\;&&z&&\;=\;&&0&\end{alignedat}}}

is a system of three equations in the three variables x, y, z. A solution to a linear system is an assignment of values to the variables such that all the equations are simultaneously satisfied. A solution to the system above is given by

{\displaystyle {\begin{alignedat}{2}x&\,=\,&1\\y&\,=\,&-2\\z&\,=\,&-2\end{alignedat}}}

since it makes all three equations valid. The word "system" indicates that the equations are to be considered collectively, rather than individually.

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