The sum of two rational numbers is -1/2. The difference is -11/10. What are the rational numbers?

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Answer 1 · 2018-03-13T23:24:49

The required rational numbers are $-4/5$ and $3/10$

Denoting the two rational numbers by $x$ and $y$ ,

From the information given,

$x + y = -1/2$ (Equation 1)
and
$x - y = -11/10$ (Equation 2)

These are just simultaneous equations with two equations and two unknowns to be solved using some suitable method.

Using one such method:

Adding equation 1 to equation 2 yields

$2x = - 32/20$

which implies

$x = -4/5$

substituting in equation 1 yields

$-4/5 + y = -1/2$

which implies

$y = 3/10$

Checking in equation 2

$-4/5 - 3/10 = -11/10$ , as expected