$$- \frac{ 1 }{ 24 } y+ \frac{ 3 }{ 2 } - \frac{ 9 }{ 14 } y=- \frac{ 1 }{ 12 } + \frac{ 2 }{ 3 } y$$
$y = \frac{266}{227} = 1\frac{39}{227} \approx 1.171806167$
$$-\frac{115}{168}y+\frac{3}{2}=-\frac{1}{12}+\frac{2}{3}y$$
$$-\frac{115}{168}y+\frac{3}{2}-\frac{2}{3}y=-\frac{1}{12}$$
$$-\frac{227}{168}y+\frac{3}{2}=-\frac{1}{12}$$
$$-\frac{227}{168}y=-\frac{1}{12}-\frac{3}{2}$$
$$-\frac{227}{168}y=-\frac{1}{12}-\frac{18}{12}$$
$$-\frac{227}{168}y=\frac{-1-18}{12}$$
$$-\frac{227}{168}y=-\frac{19}{12}$$
$$y=-\frac{19}{12}\left(-\frac{168}{227}\right)$$
$$y=\frac{-19\left(-168\right)}{12\times 227}$$
$$y=\frac{3192}{2724}$$
$$y=\frac{266}{227}$$
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