Question

Solve by elimination method:
$x + \frac{y}{2} = 4 \: and \: \frac{x}{3} + 2y = 5$
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Answer 1

First Equation :

$\mathrm{\clubsuit\;\;\;x + \dfrac{y}{2} = 4}$

$\mathrm{\longrightarrow \dfrac{2x + y}{2} = 4}$

$\mathrm{\longrightarrow 2x + y = 8\;----\;(1)}$

Second Equation :

$\mathrm{\clubsuit\;\;\;\dfrac{x}{3} + 2y= 5}$

$\mathrm{\longrightarrow \dfrac{x + 6y}{3} = 5}$

$\mathrm{\longrightarrow x + 6y = 15}$

Multiply above equation with 2

$\mathrm{\longrightarrow 2x + 12y = 30\;-----\;(2)}$

Subtract Equation (1) from Equation (2)

$\mathrm{\longrightarrow [2x + 12y] - [2x + y] = 30 - 8}$

$\mathrm{\longrightarrow 2x + 12y - 2x - y = 22}$

$\mathrm{\longrightarrow 11y = 22}$

$\mathrm{\longrightarrow y = 2}$

Substitute value of y in Equation (1) to get the value of x

$\mathrm{\longrightarrow 2x + 2 = 8}$

$\mathrm{\longrightarrow 2x = 8 - 2}$

$\mathrm{\longrightarrow 2x = 6}$

$\mathrm{\longrightarrow x = 3}$

$\mathbf{\therefore\;\;x = 3\;\;and\;\;y = 2}$