I found part a but I need help on the steps in part b

Question

the equations below represent the supply and the demand, in some order, for a certain product.

Note that the price 𝑝p is in dollars.

350𝑝+𝑞−7000=0350p+q−7000=0

𝑞−150𝑝+1350=0q−150p+1350=0

(a) Find the equilibrium point:

Quantity 𝑞=q= 1155 .

Price 𝑝=p= $16.7

(b) Suppose a tax of $3 per unit is imposed on the supplier.

Find the new equilibrium point.

Quantity 𝑞=q=  .

Price 𝑝=p= $

Answer 1

1st equation is demand with an inverse relation between price and quantity demanded

2nd equation is the supply curve with a direct relation between price and quantity supplied

solve each for p

then set them equal and solve for q

or solve with substitution elimination or matrix algebra

p=-q/350 + 7000/350 = -q/350 + 20 is the demand curve

p = q/150 + 1350/150 = q/150 + 9 is the supply curve

q/150+9=-q/350 +20

q/150 +q/350 = 20-9

q/15 +q/35 = 110

multiply by 5(7)(3)

7q +3q = 110(105)

q= 11(105) = 1155= equilibrium quantity when sales = purchases, quantity supplied = quantity demanded, and there is no shortage or surplus

p = q/150+9 = 1155/150 +9 = 7.7+9 = $16.70 = equilibrium price

if there's a tax of $3, shift the supply curve up by 3 and set the new supply curve = demand curve

q/150 +9+ 3 = -q/350 +20

q/150 +q/350 = 20-9-3 =8

q/15 +q/35 = 80

multiply by 5(3)(7)

7q+3q =80(5)3)(7)

q= 80(5)(3)(7)/10=8(105)= 840= new equilibrium quantity

p= 840/150 +12= 84/15+12=28/5+12= 5.3+12= $17.30 = new equiibrium orice

supplier passed on 60 cents to the consumer

graphing the lines may help

just shift the supply line vertically up by 3