J&J Citrus Company completes the preparation of its products by cleaning, filling, and labeling bottles. Each case of lemonade requires 12 minutes for cleaning, 4 minutes for filling, and 1 minute for labeling. Each case of pineapple juice requires 9 minutes for cleaning, 6 minutes for filling, and 1 minute for labeling. Each case of orange juice requires 10 minutes for cleaning, 4 minutes for filling, and 2 minutes for labeling. If the company ran the cleaning machine for 398 minutes, the filling machine for 164 minutes, and the labeling machine for 58 minutes, how many cases of each type of juice were prepared?

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.