Question 283474
"Two numbers" suggests we use 'x' and 'y'.
However, we are told they sum to 55:  x + y = 55
That means we can substitute 55-x for y.
That, in turn, means we have only one unknown to solve.
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We also are told that x*y = 600
Substituting y = 55-x
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x*(55-x) = 600
55x -x^2 = 600
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Add x^2 to both sides
55x = x^2 + 600
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Subtract 55x from both sides
0 = x^2 -55x + 600
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Factor
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(x-15)(x-40)=0
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So we we have two possible values for x:  15 and 40.
That means we have two possible values for y: 
55-15 = 40 and 
55-40 = 15.
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Answer:
The two numbers are 15 and 40.  Their sum is 55.  Their product is 600.
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Done.