Question

What is the solution to this system of linear equations? 2x + 3y = 3 7x – 3y = 24

Answer 1

$\large\mathsf{Hoy !!}$

$\mathsf{Given \ equations \ :}$

$\mathsf{2x + 3y \ = \ 3}$ _____( 1 )

$\mathsf{7x - 3y \ = \ 24}$

$\mathsf{Add \ both \ these \ equations}$

$\mathsf{( \ 2x + 3y \ ) + ( \ 7x - 3y \ ) \ = \ 3 + 24}$

$\mathsf{Opening \ ( \ ) \ brackets}$

$\mathsf{2x + 3y + 7x - 3y \ = \ 27}$

$\mathsf{2x + {\cancel{3y}} + 7x - {\cancel{3y}} \ = \ 27}$

$\mathsf{9x \ = \ 27}$

$\mathsf{x \ = \ {\dfrac{27}{9}}}$

$\mathsf\red{x \ = \ 3}$

$\mathsf{Put \ this \ in}$ ( 1 )

$\mathsf{2 \ ( \ 3 \ ) \ + 3y \ = \ 3}$

$\mathsf{6 + 3y \ = \ 3}$

$\mathsf{3y \ = \ 3 - 6}$

$\mathsf{3y \ = \ - \ 3}$

$\mathsf{y \ = \ {\dfrac{- \ 3}{3}}}$

$\mathsf\red{y \ = \ - \ 1}$

$<b><i>$
This method is known "Elimination Method".

In this method, one variable is eliminated.

^^"