$$5x+7y=\frac{9}{10}.$$
$x=-\frac{7y}{5}+\frac{9}{50}$
$$5x=\frac{9}{10}-7y$$
$$\frac{5x}{5}=\frac{\frac{9}{10}-7y}{5}$$
$$x=\frac{\frac{9}{10}-7y}{5}$$
$$x=-\frac{7y}{5}+\frac{9}{50}$$
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$y=-\frac{5x}{7}+\frac{9}{70}$
$$7y=\frac{9}{10}-5x$$
$$\frac{7y}{7}=\frac{\frac{9}{10}-5x}{7}$$
$$y=\frac{\frac{9}{10}-5x}{7}$$
$$y=-\frac{5x}{7}+\frac{9}{70}$$
