Question

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

Answer 1

We are given both equations, in order to find the interception point of these lines we equal their values

`\begin{gathered} 8x+386=-6x+708 \\ 8x+6x=708\text{ - 386} \\ 14x\text{ = 322} \\ x=23 \end{gathered}`

We now use this value for x and replace it in either equation

`\begin{gathered} y=8x+386 \\ y=8(23)+386 \\ y=570 \end{gathered}`

Therefore, the interception point of these lines is (23,570)

This interception point is the equilibrium point, the question states that y is the number of items produced and x is their price, because of that, we have that the selling price is $23/item and the amount of items is 570