Supply-and-demand analysis can also involve more than two interrelated markets. Use the elimination method to find Pe and Qe for each of the three markets, given the system of equations:

For equilibrium in each market,

This leaves three equations with three unknowns:

To solve a 3 × 3 system, the following hints generally prove helpful: (1) using any two of the equations, eliminate one of the three variables; (2) then, using the third equation and either of the others already used, eliminate the same variable as before; (3) this will leave two equations with two unknowns, which can then be solved by now familiar methods, as shown below.
(1) Selecting P2 for elimination and multiplying (4.44) by 2,

Subtracting (4.47) from (4.46),

(2) Now multiplying (4.46) by 3,

and adding it to (4.45), the previously unused equation,

(3) This leaves two equations with two unknowns:

which can be solved with earlier methods, giving

Then substituting P1 = 4, P3 = 6 in (4.44), (4.45), or (4.46),

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$2 Qs = 6P-8 Qs2 = 3P2-11 283 = 3P3-5 Qd =-5P + P+ P3 + 23- Qd2 P1-3P2+2P3 + 15 Qd3 P1+2P2 - 4P3 + 19