3[ Systems of linear equations]

Six circles were sequentially connected by segments. A number was written on each segment, and in each circle - the sum of the two numbers written on the segments entering it. After that, all the numbers on the segments and in one of the circles were erased (see fig.). Can the number erased in the circle be found?

![](https://cdn.mathpix.com/cropped/2024_05_06_46af0608f2d2cb90d801g-21.jpg?height=388&width=423&top_left_y=2350&top_left_x=818)

#
We will color the circles, alternating between two colors, white and black. Then each segment will enter once into a circle of each color, so the sum of the numbers in the white circles will be equal to the sum of the numbers in the black circles (each of them is equal to the sum of all the numbers written on the segments). From this, it is clear that the erased number is equal to \(a + c + e - (b - d)\).

## Answer

It is possible.