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Check it out! 1 2.2.2: Solving Systems of Linear Equations Benito is a waiter. He earns a base salary of $1,500 a month, plus 20% of the price of the meals he serves. 1. Write an equation to predict the amount of money Benito will earn if he serves $350 in meals. 2. Benito earned $1,650 in one month. What was the total price of the meals that Benito served? 3. Create a graph to show the possible amount of money Benito could earn each month. 2 2.2.2: Solving Systems of Linear Equations 1. Write an equation to predict the amount of money Benito will earn if he serves $350 in meals. • Translate the verbal description of Benito’s pay into an algebraic equation. • Let x represent the total cost of the meals Benito serves. • Let y represent the amount of money Benito earns. • Benito earns a base salary of $1.500, plus 20% of the price of the meals. • 20% of the price of the meals is 0.20x. y = 1500 + 0.20x 3 2.2.2: Solving Systems of Linear Equations • • Benito served $350 in food. Substitute $350 for x and solve the equation for y, the amount of money Benito will earn. y = 1500 + 0.20x Original equation y = 1500 + 0.20(350) Substitute 350 for x. y = 1500 + 70 Simplify. y = 1570 • Benito will earn $1,570 if he serves $350 worth of food. 4 2.2.2: Solving Systems of Linear Equations 2. Benito earned $1,650 in one month. What was the total price of the meals that Benito served? • Use your equation from part 1 to find the price of the meals Benito served. • Substitute $1,650 for y, the total amount of money Benito earned. 1650 = 1500 + 0.20x 5 2.2.2: Solving Systems of Linear Equations • Solve for x. 1650 = 1500 + 0.20x Original equation 150 = 0.20x Subtract 1,500 from both sides. 750 = x Divide both sides by 0.20. • Benito served $750 worth of meals. 6 2.2.2: Solving Systems of Linear Equations 3. Create a graph to show the possible amount of money Benito could earn each month. • The equation y = 1500 + 0.20x can be graphed using slope-intercept form. • The slope of the equation is 0.20. • The y-intercept is 1,500. 7 2.2.2: Solving Systems of Linear Equations 8 2.2.2: Solving Systems of Linear Equations