Why is 12 inches 1 foot a conversion factor ?

I have no better answer than simply, because there are 12 inches in a foot.

By definition a conversion factor is one unit being used to express a group or multiple of another unit. Just like how there are 12 of anything in one dozen. 100 years in one century. 365 days in one year. 100 centimeters in a meter. 4 quarts in one gallon. 10 dimes in one dollar. They are equal to each other and, thus, can be used as conversion factors.

this linear equation would have just one solution.

step-by-step explanation:

the reason why this would have one solution is that it is an expression with just one variable. since that variable is not raised to a power, it will always have just one solution.