|х-4|+|у+7|=0

To solve the equation \(|x-4| + |y+7| = 0\), we need to consider the properties of absolute values.

The absolute value of a number is always non-negative, so \(|x-4|\) and \(|y+7|\) are each greater than or equal to 0. The only way their sum can be 0 is if both \(|x-4| = 0\) and \(|y+7| = 0\).

This gives us:

1. \(x-4 = 0\) which means \(x = 4\).
2. \(y+7 = 0\) which means \(y = -7\).

Thus, \(x = 4\) and \(y = -7\).