Question
Solve the given pair of linear equation by the elimination method and the substitution method: $x + y = 5$ and $2x - 3y = 4$

Answer

$y = 5 .......... (1)$
$2x - 3y=4 ............. (2)$
  1. Elimination method:
    Multiplying equation $(1)$ by $2,$ we get equation $(3)$
    $2x +2y =10 ............. (3)$
    $2x−3y =4 ........... (2)$
    Subtracting equation $(2)$ from $(3),$ we get
    $5y =6 ⇒ y = \frac{6}{5}$
    Putting value of $y$ in $(1),$ we get
    $x + \frac{6}{5}=5$
    $⇒ x =5− \frac{6}{5} =  \frac{{19}}{5}$
    Therefore,$ x = \frac{{19}}{5}$ and $y = \frac{6}{5}$
  2. Substitution method:
    $x +y =5 .......................... (1)$
    $2x−3y =4 ......................... (2)$
    From equation $(1),$ we get,
    $x =5−y$
    Putting this in equation $(2),$ we get
    $2(5−y )−3y =4$
    $⇒ 10−2y−3y =4$
    $⇒ 5y =6$
    $⇒ y = \frac{6}{5}$
    Putting value of $y$ in $(1),$ we get
    $x =5−\frac{6}{5}$=$\frac{{19}}{5}$
    Therefore, $x = \frac{{19}}{5}$ and $y = \frac{6}{5}$

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