Problem in joining two objects

[Aigorlaxy]

Hello! I'm using Illustrator to design cut lines to my vinyl cutter and I'm having problems with overlaping lines.

For example, I want that three retangles to be cut using the same lines. If every retangle have its own line, I'll have double lines that will make the cutter to cut twice. I want them to share the same line.

But, I'm not being able to do that. I'm here for hours and Ctrl J doesn't work and I don't know why. I want simply to connect the bottom retangle to the two top retangles 

[Larry G. Schneider]

One way might be to Direct Select and delete the long edge closest to the other rectangles and then move the three-side rectangle so the two anchors land on the line. 

[Jacob Bugge]

Aigorlaxy,

Your three rectangles are just a wee but crucial bit more complicated than the Haus vom Nikolaus, so you need two cut lines, one for the two upper rectangles which also includes the top of the lower rectangle, and one for the sides and bottom of the lower rectangle.

You can do it in this order, or the reverse, depending on which is better for the cutting process:

The first line can start at the middle of the top, running down between the two upper rectangles, then along the bottom (also covering half the top of the lower rectangle) and up the outer side of either, then up the outer side, then all the way along the top of both upper rectangles (passing the starting point) and down the outer side of the other upper rectangle and along the bottom (also covering the other half of the top of the lower rectangle) to end at the middle of the bottom to meet the first corner.

The second line can start at either top corner of the lower (at the bottom of the corresponding upper rectangle), running down the side, along the bottom, and end at the top of the other side (at the bottom of the other upper rectangle).

With this order, each of the upper rectangles will be cut free in its entirety, and the lower rectangle will be cut from the remaining sheet.

With the opposite order, the lower rectangle will be partially cut (on three sides) and remain attached to the sheet until half of its top is cut free along with the bottom of the second of the upper rectangles.

[Met1]

You can't have a three way anchor in Illy.

Delete one of the vertical lines between the two touching rectangles.

Complete the bottom rectangle. (There's no top).

Align so that the bottom of "the two", touch the top of "the one".

Delete the two bottom strokes of the "the two". Select bottom left hand of left box with pen tool, click on top left of bottom box.

Do the same for the other side.

All the cutter is interested in is the lines, it doesn't care if they're a complete box or not. (Well, not with my soft, FineCut9)