Answer:
B: 4 solutions
Step-by-step explanation:
Combining the two equations results in 2x² = 52, or x² = 26.
This equation has two solutions: x = ±√26.
As before, x² = 26. If we substitute 26 for x² in the 1st equation, we get:
26 - 4y² = 16, or 4y² = 10, or y = ±√5/2. Again: two solutions.
If we take x to be +√26, y could be ±√(5/2).
Check: is ( √26, √(5/2) ) a solution of the system?
Subbing these values into the first equation, we get:
26 - 4(5/2) = 16. Is this true?
Then 10 = 10. Yes.
Through three more checks, we find that this system has FOUR solutions.
Consecutive numbers can be written as such:
n + (n + 1) = 73
Open the parentheses and simplify:
2n + 1 = 73
Subtract 1 from both sides:
2n = 72
Divide both sides by 2:
n = 36
The numbers are 36 and 37
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