00:01
This problem says if the demand function for a commodity is given by the equation p squared plus 4q equals 1 ,600, and the supply function is given by the equation 900 minus p squared plus 10q equals zero.
00:12
Find the equilibrium quantity and equilibrium price, and we're going to round our answers to two decimal places.
00:18
So when we go to solve this, we can see that we have a p square that's positive and a p square that's negative.
00:26
So we could almost immediately combine our two equations to begin solving a system using elimination.
00:33
But what i am going to do first is move this 900 over to the other side of the equation.
00:38
That way we have our constants lined up too.
00:40
So i'd have to subtract it over and that would replace this zero with negative 900.
00:45
So now we have constants lined up, p values lined up, and q values lined up.
00:52
And we can start again by using elimination to get rid of p -square.
00:56
P squared minus p squared eliminates.
00:59
4q plus 10q gives us 14q, and then 1 ,600 minus 900 would give us 700.
01:05
So when we divide by 14, that gives us a q value of 50.
01:14
And if we have q, we can plug in for p, and we can plug in for either equation, but i'm going to plug into the top equation.
01:21
So p squared plus 4 times the q value of 50 equals 1 ,600...