Determine whether the following conjecture is true or false. Give a counterexample if the answer is false.
1 answer:
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Let x = greater number
y = smaller number
(1)
(1)
(2)
We'll substitute y in (1) to (2)
(2)
x - 9 = 0 or x + 3 = 0
x = 9 x = -3
and
y = x - 6 y = x - 6
y = 9 - 6 y = -3 - 6
y = 3 y = -9
Therefore, the two numbers can be 9 and 3 or -3 and -9.
y = smaller number
(1)
(1)
(2)
We'll substitute y in (1) to (2)
(2)
x - 9 = 0 or x + 3 = 0
x = 9 x = -3
and
y = x - 6 y = x - 6
y = 9 - 6 y = -3 - 6
y = 3 y = -9
Therefore, the two numbers can be 9 and 3 or -3 and -9.
