306 Chapter 3 Systems of Linear Equations and Inequalities Applications of Systems of Linear Equations in Two Variables Key Concepts Solve application problems by using systems of linear equations in two variables. • Cost applications • Mixture applications • Principal and interest applications • Uniform motion applications • Geometry applications Steps to Solve Applications: 1. Label two variables. 2. Construct two equations in words. 3. Write two equations. 4. Solve the system. 5. Write the answer. Examples Example 1 Mercedes borrowed $1500 more from a lender that charges 6.5% interest than she did from a lender that charges 4% interest. If the total interest owed at the end of 1 yr is $622.50, find the amount she borrowed at 6.5%. Let x represent the amount borrowed at 6.5%. Let y represent the amount borrowed at 4%. ° Interest owed from 6.5% account ¢ ° interest owed from 4% account x y 1500 0.065x 0.04y 622.50 Using substitution gives 0.0651y 15002 0.04y 622.50 0.065y 97.5 0.04y 622.50 0.105y 525 y 5000 x 150002 1500 6500 Mercedes borrowed $6500 at 6.5%. ¢ $622.50 aAmount borrowed at 6.5% b aamount borrowed at 4% b $1500 Section 3.4
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