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The video tutorial demonstrates how to change the subject of a formula by rearranging an equation to solve for a specific variable. In the first example, the equation y = x + 8 is shown, with the goal of making x the subject. By subtracting both sides by 8, the equation is rearranged to x = y - 8. In a second example, the equation x + y = 3 is used, with the process of making x the subject shown by adding x to both sides. The final result is x + y = 3.