1. Interest problems Using Systems of Equations

2. Interest Problems Ann invested $12,000 in two bank accounts
Interest Problems Ann invested $12,000 in two bank accounts.  One of the accounts pays 6% annual interest, and the other account pays 5% annual interest.  If the combined interest earned in both accounts after a year was $700, how much money was invested in each account?
Step 1 You must assign variables x = amount invested at 6% $12,000 = total money invested in both accounts y = amount invested at 5% $700 = total interest earned in both accounts

3. Step 2 Equations must be properly set up!
x y = 12,000
.06x + .05y = 700

4. System of Equations

5. Making the Equations Nice
x + y = 12, > x + y = 12,000
.06x + .05y = > x + 5y = 70,000

6. Methods to Solve a System of Linear Equations
Graphing: paper, desmos, graphing calculator
Elimination
Substitution
Matrix Algebra

7. Step 3 Solve using Elimination Method
x + y = 12,000 -> times -6 -> -6x – 6y = x + 5y = 70,000 -> no change -> + 6x + 5y = 70,000 -y = -2,000 y = 2,000 therefore x = 10,000 Step 4 - Summarize $10,000 was invested at 6% $2,000 was invested at 5%

8. Substitution Method
x + y = 12,000 -> x = 12,000 – y solve for either variable in first equation 6x + 5y = 70,000 leave the other equation alone No substitute altered equation 1 into equation 2 6 ( 12,000 – y ) + 5y = 70,000 72,000 – 6y + 5y = 70,000 72,000 – y = 70,000 - y = y = 2,000 therefore x = 10,000

10. System of Equations ixl.com Algebra 1 skill U1,U2,U8,U10 to 50
Casey invested $20,000 in two bank accounts.  One of the accounts pays 8% annual interest, and the other account pays 7% annual interest.  If the combined interest earned in both accounts after a year was $1,525, how much money was invested in each account?
Step 1 Assign Variables
Step 2 Set up Equations
Step 3 Solve Equations using elimination or substitution method (check with graphing method)
Step 4 Summarize
System of Equations ixl.com Algebra 1 skill U1,U2,U8,U10 to 50
Due Tuesday, August 28 by 5 PM
When done continue with ixl sections A, B, C to 50