Solve for $x$ & $y$ :: $2 x + y = 8, x + 6 y = 15$

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Solution

We have
$2 x + y = 8$ ..............(i)
$x + 6 y = 15$ ............(ii)

Multiply $2$ in equation (ii) and subtract from (i)

$2 x + y = 8$
$2 x + 12 y = 30$
$(-)$ $(-)$ $(-)$
$¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯ - 11 y = - 22$
$y = 2$

put $y = 2$ in equation (1)
$2 x + 2 = 8$
$2 x = 6$
$x = 3$
So $x = 3$ and $y = 2$ is Answer.

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