Please answer showing all steps required to get to the solution including elimination of variables. If using an identity to simplify the equations, please clearly denote what the identity is and how the identity translates into the final results.

Given two competitive goods markets where in the first market demand is (D₁= a-bP₁-cP₂) and supply is (S₁= dP₁ - e + gP₂₎ and in the second market demand is (D₂ = h - jP₁-kP₂₎and supply is given by (S₂= nP₂ - m) , answer the following (assume, e and m are constants):

1. What is the general equilibrium condition?
2. What is the quantity demanded in the 1^st market?
3. What is the quantity demanded in the 2^nd market?
4. What is the price of good 1 (P₁) at equilibrium?
5. What is the price of good 2 (P₂) at equilibrium?
6. What are the conditions for a solution to exist?