Question

Please I need help!!!




Find the values of x and y:

243x + 341y = 294

341x + 243y = 290​

Answer 1

$\underline{\textsf{Given:}}$

$\mathsf{243x+341y=294}$

$\mathsf{341x+243y=290}$

$\underline{\textsf{To find:}}$

$\textsf{The values of x and y}$

$\underline{\textsf{Solution:}}$

$\textsf{Consider,}$

$\mathsf{243x+341y=294}$

$\mathsf{341x+243y=290}$

$\textsf{Adding the given equations, we get}$

$\mathsf{584x+584y=584}$

$\implies\mathsf{x+y=1}\;$.......(1)

$\textsf{Subtracting the given equations, we get}$

$\mathsf{-98x+98y=4}$

$\mathsf{-49x+49y=2}\;$........(2)

$\textsf{Now using (1) in (2)}$

$\mathsf{-49x+49(1-x)=2}\;$

$\mathsf{-49x+49-49x=2}\;$

$\mathsf{-98x=2-49}\;$

$\mathsf{-98x=-47}\;$

$\implies\mathsf{x=\dfrac{47}{98}}\;$

$\textsf{From (1)}$

$\implies\mathsf{y=1-\dfrac{47}{98}}\;$

$\implies\mathsf{y=\dfrac{98-47}{98}}\;$

$\implies\mathsf{y=\dfrac{51}{98}}\;$

$\underline{\textsf{Answer:}}$

$\mathsf{x=\dfrac{47}{98},\;y=\dfrac{51}{98}}$

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