Question

The supply curve for steel is 90x−y=−50. The demand curve is 10x+y=200. x is quantity in thousands of metric tons y is price in dollars per metric ton What are the values for quantity and price at the intersection point of the two curves? To find the values, first use addition to combine the left sides and to combine the right sides of the two equations.

Answer 1

The intersection point of the two curves is
`(x,y) = \left((3)/(2)\,kton.m, 185\,USD \right)`.

Explanation:

From statement we get the following equations:

Supply curve

`90\cdot x - y = -50` (1)

Demand curve

`10\cdot x + y = 200` (2)

Where:

`x` - Quantity, measured in thousands of metric tons.

`y` - Price, measured in US dollars per metric tons.

If we add both equations, then we find that quantity is:

`(90\cdot x -y )+(10\cdot x +y) = -50+200`

`100\cdot x = 150`

`x = (3)/(2)\,kton.m`

Then, we finally find the price by substituting on (2):

`y = 200-10\cdot \left((3)/(2) \right)`

`y = 200-15`

`y = 185\,USD`

The intersection point of the two curves is
`(x,y) = \left((3)/(2)\,kton.m, 185\,USD \right)`.