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The sum of two numbers is 5 and the larger difference of the two numbers is 39 find the two numbers by setting up a system of equations with two unknowns and solving algebraically

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The larger number is 22 while the smaller number is -17.

Let x represent the larger number and y represent the smaller number.

The sum of two numbers is 5, hence:

x + y = 5      (1)

The larger difference of the two numbers is 39, hence:

x - y = 39     (2)

Solving equations 1 and 2 simultaneously gives:

x = 22, y = -17

Therefore the larger number is 22 while the smaller number is -17.

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