If 1/x + 1/y = 3 and 1/x - 1/y = 7, what is the value of x + y? Express your answer as a common fraction.
+1223 Let \(\frac{1}{x} = a\) and \(\frac{1}{y} = b..\)
We can rewrite the system like so:
a + b = 3
a - b = 7
Adding, we get a = 5 and b = -2, which means that x = 1/5 and y = -1/2.
x + y = -3/10
