Question

Solution+of+3y/2-5x/3=-2+and+y/3+x/3=13/16+by+elimination+method

Answer 1

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

$\mathsf{\dfrac{3y}{2}-\dfrac{5x}{3}=-2}$

$\mathsf{\dfrac{y}{3}+\dfrac{x}{3}=\dfrac{13}{16}}$

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

$\textsf{The solution of the given equations by elimination method}$

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

$\textsf{The given equations can be written as}$

$\mathsf{-10x+9y=-12}$......(1)

$\mathsf{16x+16y=39}$.......(2)

$\mathsf{(1){\times}16\implies-160x+144y=-192}$

$\mathsf{(2){\times}10\implies\,160x+160y=390}$

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

$\mathsf{304y=198}$

$\mathsf{y=\dfrac{198}{304}}$

$\boxed{\mathsf{y=\dfrac{99}{152}}}$

$\textsf{Put}\;\mathsf{y=\dfrac{99}{152}}\,\textsf{in (1)}$

$\mathsf{-10x+9(\dfrac{99}{152})=-12}$

$\mathsf{-10x+\dfrac{891}{152}=-12}$

$\mathsf{-10x=-12-\dfrac{891}{152}}$

$\mathsf{-10x=\dfrac{-1824-891}{152}}$

$\mathsf{-10x=\dfrac{-2715}{152}}$

$\mathsf{2x=\dfrac{543}{152}}$

$\boxed{\mathsf{x=\dfrac{543}{304}}}$

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

$\textsf{Solution is}$

$\mathsf{x=\dfrac{543}{304}\;\&\;y=\dfrac{99}{152}}$

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