In supply (and demand) problems, y is the number of items the supplier will produce (or the public will buy) if the price of the item is x.
For a particular product, the supply equation is y=5x+465 and the demand equation is y=−6x+652.

A) What is the intersection point of these two lines?(enter answer an an ordered pair) __

B) What is the selling price when supply and demand are in equilibrium? price=$_/item

C)What is the amount of items in the market when supply and demand are in equilibrium?
number of items =_________

First we must calculate the intersection point of the two lines. Since in that point y has the same value in both equations, we can obtain x by equalling the two equations and then using that value for obtaining y:

[tex]5x+465=-6x+652\\5x+6x=652-465\\11x=187\\x=\frac{187}{11}\\x=17[/tex]

So the value of x in the intersection point is 17. We now use this value with either one of the equations to obtain y. Let's use the supply equation:

[tex]y=5*17+465\\y=550[/tex]

So the intersection point is (17 ; 550)

Supply and demand are in equilibrium when the amount of items on supply are the same as the ones on demand. That is the point were the two lines intersect, which means the selling price is the x coordinate and the amount of items is the y coordinate, so that is a selling price of $17/item with a number of items of 550.