Question

For the pair of supply-and-demand equations, where x represents the quantity demanded in units of 1000 and p is the unit price in dollars, find the equilibrium quantity and the equilibrium price.

2x + 9p − 90 = 0 and 3x − 11p + 61 = 0

Answer 1

the equilibrium quantity is 9,000 units (since x represents quantity demanded in units of 1000) and the equilibrium price is $8.

Explanation:

2x + 9p - 90 = 0

3x - 11p + 61 = 0

To solve this system, we can use the method of substitution or elimination. Let's use the method of elimination.

Multiply the first equation by 11 and the second equation by 9 to make the coefficients of p in both equations equal:

22x + 99p - 990 = 0

27x - 99p + 549 = 0

Add the two equations together:

(22x + 99p - 990) + (27x - 99p + 549) = 0 + 0

Combine like terms:

49x - 441 = 0

Add 441 to both sides:

49x = 441

Divide both sides by 49:

x = 9

Substitute this value of x into one of the original equations, let's use the first equation:

2(9) + 9p - 90 = 0

Simplify:

18 + 9p - 90 = 0

Combine like terms:

9p - 72 = 0

Add 72 to both sides:

9p = 72

Divide both sides by 9:

p = 8