Question

Solve the equations by substitution method : 2 x = 5 y + 12 ; 3 x – 2 y + 4 = 0.

Answer 1

Given

$2x=5y+12$

$\implies x = \dfrac{5y+12}{2}$

Substituting x in the second equation, we get,

$3x-2y+4=0$

$\implies 3(\dfrac{5y+12}{2} ) -2y+4=0$

$\implies \dfrac{15y+36}{2} -2y+4=0$

Multiplying the entire equation by 2, we get,

$\implies 15y+36-4y+8=0$

$\implies 11y+44=0$

$\implies 11y = -44$

$\implies y = \dfrac{-44}{11}$

$\implies y = -4$

Substituting the value of y, we get,

$x = \dfrac{20+12}{2}$

$\implies x = \dfrac{32}{2}$

$\implies x = 16$

$\boxed{\boxed{\bold{Therefore, \ the \ values \ of \ x \ and \ y \ are \ 16 \ and \ -4 \ respectively}}}}}$