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## Sagot :

The demand function is given by:

[tex]\[ P = -Q + 34 \][/tex]

The supply function is given by:

[tex]\[ P = Q - 10 \][/tex]

At equilibrium, the quantity demanded equals the quantity supplied. Therefore, we set the two equations equal to each other:

[tex]\[ -Q + 34 = Q - 10 \][/tex]

Next, we solve for [tex]\(Q\)[/tex]:

1. Add [tex]\(Q\)[/tex] to both sides:

[tex]\[ 34 = 2Q - 10 \][/tex]

2. Add 10 to both sides:

[tex]\[ 44 = 2Q \][/tex]

3. Divide by 2:

[tex]\[ Q = 22 \][/tex]

Now that we have the equilibrium quantity, we substitute [tex]\(Q = 22\)[/tex] back into either the demand or supply function to find the equilibrium price [tex]\(P\)[/tex]. Using the supply function:

[tex]\[ P = Q - 10 \][/tex]

[tex]\[ P = 22 - 10 \][/tex]

[tex]\[ P = 12 \][/tex]

Therefore, the equilibrium point is [tex]\((22, 12)\)[/tex].

The correct answer is:

D. [tex]\((22, 12)\)[/tex]