the equilibrium point, is when Demand = Supply, namely, when the amount of "Q"uantity demanded by customers is the same as the Quantity supplied by vendors.
That occurs when both of these equations are equal to each other.
let's do away with the denominators, by multiplying both sides by the LCD of all fractions, in this case, 12.
![\bf \stackrel{\textit{Supply}}{-\cfrac{3}{4}Q+35}~~=~~\stackrel{\textit{Demand}}{\cfrac{2}{3}Q+1}\implies \stackrel{\textit{multiplying by 12}}{12\left( -\cfrac{3}{4}Q+35 \right)=12\left( \cfrac{2}{3}Q+1 \right)} \\\\\\ -9Q+420=8Q+12\implies 408=17Q\implies \cfrac{408}{17}=Q\implies \boxed{24=Q} \\\\\\ \stackrel{\textit{using the found Q in the Demand equation}}{P=\cfrac{2}{3}(24)+1}\implies P=16+1\implies \boxed{P=17} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \stackrel{Equilibrium}{(24,17)}~\hfill](https://tex.z-dn.net/?f=%5Cbf%20%5Cstackrel%7B%5Ctextit%7BSupply%7D%7D%7B-%5Ccfrac%7B3%7D%7B4%7DQ%2B35%7D~~%3D~~%5Cstackrel%7B%5Ctextit%7BDemand%7D%7D%7B%5Ccfrac%7B2%7D%7B3%7DQ%2B1%7D%5Cimplies%20%5Cstackrel%7B%5Ctextit%7Bmultiplying%20by%2012%7D%7D%7B12%5Cleft%28%20-%5Ccfrac%7B3%7D%7B4%7DQ%2B35%20%5Cright%29%3D12%5Cleft%28%20%5Ccfrac%7B2%7D%7B3%7DQ%2B1%20%5Cright%29%7D%20%5C%5C%5C%5C%5C%5C%20-9Q%2B420%3D8Q%2B12%5Cimplies%20408%3D17Q%5Cimplies%20%5Ccfrac%7B408%7D%7B17%7D%3DQ%5Cimplies%20%5Cboxed%7B24%3DQ%7D%20%5C%5C%5C%5C%5C%5C%20%5Cstackrel%7B%5Ctextit%7Busing%20the%20found%20Q%20in%20the%20Demand%20equation%7D%7D%7BP%3D%5Ccfrac%7B2%7D%7B3%7D%2824%29%2B1%7D%5Cimplies%20P%3D16%2B1%5Cimplies%20%5Cboxed%7BP%3D17%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20%5Crule%7B34em%7D%7B0.25pt%7D%5C%5C%5C%5C%20~%5Chfill%20%5Cstackrel%7BEquilibrium%7D%7B%2824%2C17%29%7D~%5Chfill)
Is there a picture to go with this? That would help me answer the question.
Step-by-step explanation:
9x²+bx+ 100
(3x)²+ bx + 10²
(3x)² + 10² + bx
(3x)² + 10² + bx