Question

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Answer 1

$\bf{\underline{Question:-}}$

Solve the following simultaneous equations.

$\sf{\dfrac{1}{3}x + \dfrac{1}{4}y = 4 ; \dfrac{5}{6}x - \dfrac{1}{8}y = 4}$

$\bf{\underline{Solution:-}}$

$\sf{\dfrac{1}{3}x + \dfrac{1}{4} y = 4 \longrightarrow (i)}$

$\sf{\dfrac{5}{6}x - \dfrac{1}{8}y = 4 \longrightarrow (ii)}$

$\sf{\underline{From\:eq.(i)}}$

$\sf{\dfrac{1}{3}x + \dfrac{1}{4} y = 4}$

= $\sf{\dfrac{4x + 3y}{12} = 4}$

$\sf{\implies 4x+3y = 4\times 12}$

$\sf{\implies 4x = 48-3y}$

$\sf{\implies x = \dfrac{48-3y}{4}}$

$\sf{\underline{Substituting\:the\:value\:of\:x\:in\:eq.(ii)}}$

$\sf{\dfrac{5}{6}x - \dfrac{1}{8}y = 4}$

= $\sf{\dfrac{5}{6}\times\dfrac{48-3y}{4} - \dfrac{1}{8}y = 4}$

$\sf{\implies \dfrac{240 - 15y}{24} - \dfrac{1}{8}y = 4}$

$\sf{\implies \dfrac{240 - 15y - 3y}{24} = 4}$

$\sf{\implies 240 - 18y = 24\times4}$

$\sf{\implies 240 - 18y = 96}$

$\sf{\implies -18y = -240 + 96}$

$\sf{\implies -18y = -144}$

$\sf{\implies y = \dfrac{-144}{-18}}$

$\sf{\implies y = 8}$

$\sf{\underline{Putting\:the\:value\:of\:y\:in\:eq.(i)}}$

$\sf{\dfrac{1}{3}x + \dfrac{1}{4}y = 4}$

= $\sf{\dfrac{1}{3}x + \dfrac{1}{4}\times 8 = 4}$

$\sf{\implies \dfrac{1}{3}x + 2 = 4}$

$\sf{\implies \dfrac{1}{3}x = 4-2}$

$\sf{\implies \dfrac{1}{3}x = 2}$

$\sf{\implies 1x = 2\times3}$

$\sf{\implies x = 6}$

$\sf{\underline{Therefore}}$

$\sf{x=6;y=8}$