Find the values of $x$ and $y$ that satisfy both the given equations.
$y - 2 x = 4$ and $y - 3 x = 2$

$(2, 8)$

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$(8, 1)$

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$(2, 4)$

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$(4, 2)$

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Solution

The correct option is A
$(2, 8)$

To find the solution of the equation, we do the following:
$y - 2 x = 4$
$\Rightarrow y = 2 x + 4$ ............(i)
Then, $y - 3 x = 2$
$\Rightarrow y = 3 x + 2$ ............(ii)

Equating the value of $y$ from both the equations:
$\Rightarrow 2 x + 4 = 3 x + 2$
$\Rightarrow x = 2$

Substituting the value of $x$ to get the value of $y$ :
$\Rightarrow y = 3 (2) + 2$
$\Rightarrow y = 8$

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