Section 3.6 Systems of Linear Equations in Three Variables and Applications 287 Clear fractions and write each equation in standard form. Multiply by 2. 2x z 20 x y 12 x y z 180 B 1 2 z 10 x 2x z 20 Pair up equations and to form a system of two D variables. Solve for x. y x 12 x y z 180 D B 2x z 120 x y z 180 3x y 200 A C Multiply by 1. x y 12 3x y 200 3x y 200 4x 188 x 47 x y 12 x y 12 47 y 12 y 59 The smallest angle measures 47, the middle angle measures 59, and the largest angle measures 74. Applying Systems of Linear Equations to Nutrition B C C B D Example 3 B C Doctors have become increasingly concerned about the sodium intake in the U.S. diet. Recommendations by the American Medical Association indicate that most individuals should not exceed 2400 mg of sodium per day. Torie ate 1 slice of pizza, 1 serving of ice cream, and 1 glass of soda for a total of 1030 mg of sodium. David ate 3 slices of pizza, no ice cream, and 2 glasses of soda for a total of 2420 mg of sodium. Emilie ate 2 slices of pizza, 1 serving of ice cream, and 2 glasses of soda for a total of 1910 mg of sodium. How much sodium is in one serving of each item? Answer 2. The sides are 8 in., 10 in., and 12 in. Standard Form A Notice equation is missing the z variable. Therefore, we can eliminate z again by pairing up equations and . A From equation we have From equation we have Skill Practice 2. The perimeter of a triangle is 30 in.The shortest side is 4 in. shorter than the longest side.The longest side is 6 in. less than the sum of the other two sides. Find the length of each side. Solution: Let x represent the sodium content of 1 slice of pizza. Let y represent the sodium content of 1 serving of ice cream. Let z represent the sodium content of 1 glass of soda. x y z 180 47 59 z 180 z 74
miller_intermediate_algebra_4e_ch1_3
To see the actual publication please follow the link above