The graphs of three functions $y=a x+a, y=b x+b$ and $y=c x+d$ have a common point, and $a \neq b$. Is it necessarily true that $c=d$?
Clearly, the point $(-1,0)$ belongs to the first two lines. Since $a \neq b$, these lines are distinct, so they have no other common points. Therefore, the point $(-1,0)$ also belongs to the graph of the third function, which means $0 = -c + d$.

## Answer

Certainly

Can a $5 \times 5$ square be cut into rectangles of two types: $1 \times 4$ and $1 \times 3$ so that exactly 7 rectangles are obtained?

## Solution

See the figure.

![](https://cdn.mathpix.com/cropped/2024_05_06_d7c3832c1c4b0d15493ag-10.jpg?height=281&width=323&top_left_y=374&top_left_x=868)

Answer

Yes, it can.

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