Question

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

Answer 1

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

Explanation:

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