To analyze the impact of a tax on equilibrium price and quantity, we can follow a systematic approach using algebra. When a tax is imposed on suppliers, it effectively shifts the supply curve. For instance, if suppliers are taxed $1 per unit, we need to adjust the supply equation accordingly.

Consider the original supply equation given by Q_s = 2P - 6 and the demand equation Q_d = 10 - P. To account for the tax, we replace the price P in the supply equation with P - tax, which reflects the reduced amount suppliers receive after the tax is deducted. In this case, the tax is $1, so the new supply equation becomes:

Q_s = 2(P - 1) - 6

Expanding this, we have:

Q_s = 2P - 2 - 6 = 2P - 8

Next, we find the new equilibrium by setting the adjusted supply equal to the demand:

2P - 8 = 10 - P

Rearranging the equation gives:

3P = 18

Thus, the equilibrium price P is:

P = 6

At this point, we can determine the equilibrium quantity by substituting the equilibrium price back into the demand equation:

Q_d = 10 - 6 = 4

Now, we need to identify the prices paid by buyers and received by sellers. The price paid by buyers, P_B, is the equilibrium price of $6. Since the suppliers are taxed $1, the price received by sellers, P_S, is:

P_S = P_B - tax = 6 - 1 = 5

In summary, after the tax is imposed, the new equilibrium price is $6, the equilibrium quantity is 4, buyers pay $6, and sellers receive $5. This analysis illustrates how taxes affect market dynamics, shifting the burden between buyers and sellers while altering the equilibrium state.