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How would I go about using cramer's rule on this system of equations?

$\frac{1}{X} + \frac{1}{Y} = 7$

$\frac{1}{X} - \frac{1}{Y} = 1$

When I multiply through by xy they don't even look like linear equations. You'll have to excuse my inexperience with mathjax. I might use it once every two years when asking a question on this site.

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    Well you could add a change of variables $1/x=a$ and $1/y=b$ it would then make it linear. You just have to take care that $a\not= 0$,$b\not= 0$ in general, though I don't think this is the case here. – 2017-02-07
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    Thanks guys. Is there a way invert an equation like this one? – 2017-02-07

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Hint -

Put a = $\frac 1X$ and b = $\frac 1Y$

We have -

a + b = 7

a - b = 1

$$D = \begin{vmatrix} 1&1\\1&-1\end{vmatrix}$$

$$D_1 = \begin{vmatrix} 7&1\\1&-1\end{vmatrix}$$

$$D_2 = \begin{vmatrix} 1&7\\1&1\end{vmatrix}$$

Then find value of a and b using Cramer rule. And on last replace values with X and Y.