Answer:
No. If 5x=y+7 then xy=6 and (2) x and y are consecutive integers with the same sign. for xy=6
Step-by-step explanation:
<u>For the sake of clarity:</u>
If 5x=y+7 then (x – y) > 0?
Alternatives:
(1) xy = 6
(2) x and y are consecutive integers with the same sign
1) Consider (x-y)>0 as true:
Numbers like, 3*2, 6*1, etc..
Since y in this hypothetical case is lesser then let's find x, let's plug in y 1 for a value lesser than 1.75:
Then xy≠6 and no and 8/5 (1.75) is a rational number. What makes false the second statement about consecutive integers.
So this is a Contradiction. (x-y) >0 is not true for 5x=x+7.
2) Consider:
x and y are consecutive integers with the same sign is true.
Algebraically speaking, two consecutive integers with the same sign can be written as:
Plugging in the first equation (5x=y+7):
5x=x+1+7⇒4x=8 ⇒x =2
Since y=3 then x=2 because:
3) Testing it