Sec. 9.3 Solving Problems with Two Variables SYSTEMS OF LINEAR EQUATIONS Sec. 9.3 Solving Problems with Two Variables

Example 1 – last semester method (one variable) John has 15 coins, all dimes and quarters, worth $2.55. How many dimes and how many quarters does John have? Last semester, we used only ONE variable. Here is how we would have solved it then. Number Value per coin Total Value Dimes x 10 10x Quarters 15-x 25 25(15-x) So John had 8 dimes and 7 quarters

Example 1 – this semester method (two variables) John has 15 coins, all dimes and quarters, worth $2.55. How many dimes and how many quarters does John have? This semester we have learned how to solve with two variables. Number Value per coin Total Value Dimes d 10 10d Quarters q 25 25q So John had 8 dimes and 7 quarters

Example 2 Ann and Betty together have $60. Ann has $9 more than twice Betty’s amount. How much money does each have? Let’s use a two variable approach since that is what we’re studying…. Ann has $43 and Betty has $17.

Let’s look at a two-variable approach…. Example 3 Joan Wu has $8000 invested in stocks and bonds. The stocks pay 4% interest, and the bonds pay 7% interest. If her annual income from the stocks and bonds is $500, how much is invested in bonds? Let’s look at a two-variable approach…. Amount Invested Interest Rate Interest Earned Stocks s .04 .04s Bonds b .07 .07b 8000 500 First equation Second equation Joan Wu invested $6000 in bonds.