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

2. Example 1 – last semester method (one variable)
John has 15 coins, all dimes and quarters, worth $ 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

3. Example 1 – this semester method (two variables)
John has 15 coins, all dimes and quarters, worth $ 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

4. 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.

5. 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.