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To solve two equations using elimination, add the equations to eliminate a variable, then solve for the remaining variable. For example, given 2x + 3y = 8 and 5x - 3y = -1, add the equations to get 7x = 7. Divide by 7 to find x = 1. Substitute x back into an equation to solve for y. In this case, y = 2. The solution is the ordered pair (1, 2).