Starting with the equation Y - 4x = 7, we can express y as y = 4x + 7. Now, substitute this expression into the second equation 2y + 4x = 2:
2(4x + 7) + 4x = 2,
which simplifies to 8x + 14 + 4x = 2. After that, we gather like terms:
12x = 2 - 14,
yielding 12x = -12, hence x = -1. Plugging x into the equation y - 4(-1) = 7 also reveals:
y + 4 = 7,
which gives y = 3. Thus, the solution arrives at (-1, 3).
Response:
Thorough analysis:
I believe that option 4 is the right choice
There will still be 34.5 L of water in the two pails combined because no water is lost.
Thus the total remains 34.5 L after transferring water between them.
Let the final amount in the smaller pail be x.
Then the larger pail contains 9x.
So x + 9x = 34.5.
That simplifies to 10x = 34.5.
Dividing both sides by 10 gives x = 3.45.
Therefore the smaller pail held 3.45 L at the end.
Because 0.68 L was poured into it, its initial volume was 2.77 L (3.45 minus 0.68)
We can also deduce the larger pail initially contained 31.73 L
(either 35 minus 2.77, or 9 times 3.45 plus 0.68)