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