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 $- \frac{4}{5}$ $-4/5$ and $\frac{3}{10}$ $3/10$

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

From the information given,

$x + y = - \frac{1}{2}$ $x + y = -1/2$ (Equation 1)
and
$x - y = - \frac{11}{10}$ $x - y = -11/10$ (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

$2 x = - \frac{32}{20}$ $2x = - 32/20$

which implies

$x = - \frac{4}{5}$ $x = -4/5$

substituting in equation 1 yields

$- \frac{4}{5} + y = - \frac{1}{2}$ $-4/5 + y = -1/2$

which implies

$y = \frac{3}{10}$ $y = 3/10$

Checking in equation 2

$- \frac{4}{5} - \frac{3}{10} = - \frac{11}{10}$ $-4/5 - 3/10 = -11/10$ , as expected