Why is it important to keep two sides of an equation balanced when solving?

2y= 3 2 x−2 y = − 1 3 x + 1 y=− 3 1 x+1

Samson is going shopping for sugar and butter to make three different kinds of cookies: lemon bars, peanut butter cookies, and sugar cookies. the recipe for lemon bars calls for 2 cups of flour, 2 cups of sugar, and 1 stick of butter. the peanut butter cookie recipe calls for 2 cups of flour, 4 cup of sugar and 2 stick of butter. the sugar cookie recipe calls for 1 cup of flour, 2 cups of sugar, and 2 sticks of butter. sampson has 13 cups of flour at home, and he buys 12 cups (6 pounds) of sugar and 10 sticks of butter. how many batches of each type of cookie can he make? samson can make batches of lemon bars, batches of peanut butter cookies, and batches of 09 cookies submit reset

The price of a dozen eggs was $1.63. suppose the price increases m dollars per dozen and then the price decreases $0.12 per dozen. which expression represents the current price of eggs after the two price changes?