Math, asked by pprasad13232, 9 months ago

in the pair of linear equations x+y=9 and x-y =1. the value of x and y are?

Answers

Answered by Mihir1001

$\huge{\underline{\mathfrak{\textcolor{blue}{Answer :}}}}$

$\huge\boxed{\fcolorbox{red}{pink}{ ( x = 5 ) and ( y = 4 ) }}$

$\huge{\underline{\mathrm{\textcolor{red}{Step-by-step \: \: explanation :}}}}$

$\LARGE{\underline{\mathtt{\textcolor{violet}{Given :-}}}}$

Two linear equations in two variables :

x + y = 9 ———————————( 1 )
x - y = 1 -———–———————( 2 )

$\LARGE{\underline{\mathtt{\textcolor{green}{To \: \: find :-}}}}$

x and y

$\LARGE{\underline{\mathtt{\textcolor{teal}{Concept \: \: used :-}}}}$

Linear Equations in Two Variables

$\LARGE{\underline{\mathtt{\textcolor{blue}{Solution :-}}}}$

method used : $\boxed{ \: Elimination \: \: Method \: }$

On adding ( 1 ) and ( 2 ) , we get :

${ \\ }$

( x ) $+ \cancel{( y )}$ = ( 9 )

( x ) $- \cancel{( y )}$ = ( 1 )

——————————————

( 2x ) + 0 = ( 10 )

——————————————

$\implies$ $\Large{2x = 10}$

$\implies$ $\Large{ {}^{1} \cancel{2} x = \cancel{10} {}^{5} }$

$\implies$ $\Large{x = 5}$

On putting x = 5 in ( 1 ) , we get :

$\longmapsto$ $\Large{( 5 ) + y = 9}$

$\implies$ $\Large{y + 5 = 9}$

$\implies$ $\Large{y = ( 9 - 5 )}$

$\implies$ $\Large{y = 4}$

$\LARGE{\underline{\mathtt{\textcolor{magenta}{Conclusion :-}}}}$

x = 5
y = 4

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