Page 246

miller_intermediate_algebra_4e_ch1_3

286 Chapter 3 Systems of Linear Equations and Inequalities A Step 5: Now that two variables are known, 2x y 3z 7 2112 y 3122 7 2 y 6 7 y 4 7 y 3 x 2y z 1 3x y 2z 13 substitute these values (x and z) into any of the original three equations to find the remaining variable y. Substitute x 1 and z 2 into equation A . Step 6: Check the ordered triple in the three original equations. 3. Applications of Linear Equations in Three Variables Applying Systems of Linear Equations to Geometry Example 2 In a triangle, the smallest angle measures 10 more than one-half the measure of the largest angle. The middle angle measures 12 more than the measure of the smallest angle. Find the measure of each angle. Solution: Let x represent the measure of the smallest angle. Let y represent the measure of the middle angle. Let z represent the measure of the largest angle. To solve for three variables, we need to establish three independent relationships among x, y, and z. x 1 2 z 10 C x y z 180 The sum of the angles inscribed in a triangle is 180°. A B y x 12 x z y The smallest angle measures 10° more than one-half the measure of the largest angle. The middle angle measures 12 more than the measure of the smallest angle. The solution set is 5(1, 3, 2)6. Check: Skill Practice Solve the system. 1. 2x 3y z 8 ✔ True ✔ True ✔ True 2x y 3z 7 2112 132 3122 7 3x 2y z 11 3112 2132 122 11 2x 3y 2z 3 2112 3132 2122 3 Answer 1. 5(1,2, 4)6


miller_intermediate_algebra_4e_ch1_3
To see the actual publication please follow the link above