Many people who face this kind of price tag wonder if they can get away with patching their pipes. But if the sewer line is old there are almost certainly water leak other bad spots that will give you problems now or in the near future. A series of patch jobs isn't cheap. In the long run, it just makes more sense to replace the entire line.
When you get to the house stand if front of the toilet and locate the water shut off valve. Should be down below the toilet on the wall. Just turn it off (righty-tighty) completely and flush the toilet. All the water should have left the tank, well at least most of it. If there is remaining water line repair get it out with paper towels or a rag. The important thing is that no more water came in. If it did then your valve is not shut all the way or not working and you need additional help.
One other common design that is considered "washerless" was made famous by Delta and copied by several other makers. It uses little "cup" seals that fit over springs recessed in the back of the valve body. The springs press these "seals" against the cartridge and regulate the flow through little tapered openings in the cartridge. If you have one of these and it's dripping, changing these springs and seals will usually correct it. Here's a tip. Once you have the cartridge out of the way, insert a phillips screwdriver into the seal and pop both the seal and spring out. Stick the new ones on the end of the screwdriver to help guide them into place. This is especially helpful if you don't have long slender fingers.
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The first step in the replacement project is to turn off the water line repair to the toilet and flush any water that may be in the tank. If you forget this step, you will have a giant mess to clean up! You should now disconnect that water line.
The way a toilet plunger works is by filling up with water and then pushing that water through the stopped up drain. When unclogging a clogged toilet, the idea is to plunge up and down a couple of times so the plunger fills with water and then jam the open end, sometimes called a force cone, into the waste outlet in the plugged toilet and start plunging. You may have to pump the plunger up and down several times to clear the blockage.
The plumber you hire does not normally do heating but will do hot water heating or in floor heating in the house. Some places you can use the water heater for both domestic hot water and for in floor heating if the heating is a secondary heat. Check with your local plumbing codes on this to be clear.