1. REVIEW 1. Solve by graphing: x – 2y = -3 y = -3x + 5 2. Solve using substitution: x – 2y = -3 y = -3x + 5 3. Solve using elimination: x – 2y = -3 y = -3x + 5

2. REVIEW 1. Solve by graphing: x – 2y = -3 y = -3x + 5 2. Solve using substitution: x – 2y = -3 y = -3x + 5 3. Solve using elimination: x – 2y = -3 y = -3x + 5 ( 1, 2) 1 st Equation: x-int = -3 1 st Equation: slope = 1 / 2

3. REVIEW 1. Solve by graphing: x – 2y = -3 y = -3x + 5 2. Solve using substitution: x – 2y = -3 y = -3x + 5 3. Solve using elimination: x – 2y = -3 y = -3x + 5 x – 2y = -3 y = -3x + 5 x – 2(-3x + 5) = -3 x + 6x – 10 = -3 7x – 10 = -3 7x = 7 x = 1 y = -3(1) + 5 y = -3 + 5 y = 2 ( 1, 2)

4. REVIEW 1. Solve by graphing: x – 2y = -3 y = -3x + 5 2. Solve using substitution: x – 2y = -3 y = -3x + 5 3. Solve using elimination: x – 2y = -3 y = -3x + 5 x – 2y = -3 y = -3x + 5 x – 2y = -3 3x + y = 5 [2] x – 2y = -3 6x + 2y = 10 7x = 7 x = 1 y = -3(1) + 5 y = -3 + 5 y = 2 ( 1, 2)

5. REVIEW The units digit of a two-digit number exceeds twice the tens digit by 1. Find the number if the sum of its digits is 10. = units digit = tens digit u t more than

6. REVIEW The units digit of a two-digit number exceeds twice the tens digit by 1. Find the number if the sum of its digits is 10. = units digit = tens digit u t The units digit twice the tens digit by 1. exceeds

7. REVIEW The units digit of a two-digit number exceeds twice the tens digit by 1. Find the number if the sum of its digits is 10. = units digit = tens digit u t The units digit exceeds twice the tens digit by 1. u = is 1 more than + 1 2 t u = 2t + 1 twice the tens digit

8. REVIEW The units digit of a two-digit number exceeds twice the tens digit by 1. Find the number if the sum of its digits is 10. = units digit = tens digit u t u = 2t + 1

9. REVIEW The units digit of a two-digit number exceeds twice the tens digit by 1. Find the number if the sum of its digits is 10. = units digit = tens digit u t u = 2t + 1 sum of its digits is 10. sum of its digitsis10.

10. REVIEW The units digit of a two-digit number exceeds twice the tens digit by 1. Find the number if the sum of its digits is 10. = units digit = tens digit u t u = 2t + 1 sum of its digitsis10. + u t = 10

11. REVIEW The units digit of a two-digit number exceeds twice the tens digit by 1. Find the number if the sum of its digits is 10. = units digit = tens digit u t u = 2t + 1 + u t = 10 u + t = 10

12. REVIEW The units digit of a two-digit number exceeds twice the tens digit by 1. Find the number if the sum of its digits is 10. = units digit = tens digit u t u = 2t + 1 u + t = 10 SUBSTITUTION 2t + 1 + t = 10 3t + 1 = 10 ADD LIKE TERMS 3t = 9 SUBT. PROP. OF EQ. t = 3 DIV. PROP. OF EQ.

13. REVIEW The units digit of a two-digit number exceeds twice the tens digit by 1. Find the number if the sum of its digits is 10. = units digit = tens digit u t u = 2t + 1 u + t = 10 SUBSTITUTION 2t + 1 + t = 10 3t + 1 = 10 ADD LIKE TERMS 3t = 9 SUBT. PROP. OF EQ. t = 3 DIV. PROP. OF EQ. u = 2t + 1 u = 2(3) + 1 u = 6 + 1 u = 7

14. REVIEW The units digit of a two-digit number exceeds twice the tens digit by 1. Find the number if the sum of its digits is 10. = units digit = tens digit u t u = 2t + 1 u + t = 10 2t + 1 + t = 10 3t + 1 = 10 3t = 9 t = 3 u = 2(3) + 1 u = 6 + 1 u = 7 How do we write the answer? 37

15. REVIEW Teresa invested $10,000, part at 6% annual interest and the rest at 8% annual interest. If she received $760 in total simple interest at the end of the year, how much did she invest at each rate? x = inv. at 6% y = inv. at 8% x + y = 10000

16. REVIEW Teresa invested $10,000, part at 6% annual interest and the rest at 8% annual interest. If she received $760 in total simple interest at the end of the year, how much did she invest at each rate? x = inv. at 6% y = inv. at 8% x + y = 10000 x + y = 10000

17. REVIEW Teresa invested $10,000, part at 6% annual interest and the rest at 8% annual interest. If she received $760 in total simple interest at the end of the year, how much did she invest at each rate? x = inv. at 6% y = inv. at 8% x + y = 10000 i = prt For one year, i = pr (pr) 6% + (pr) 8% = Total Interest x(.06)+ y(.08) = 760

18. REVIEW Teresa invested $10,000, part at 6% annual interest and the rest at 8% annual interest. If she received $760 in total simple interest at the end of the year, how much did she invest at each rate? x = inv. at 6% y = inv. at 8% x + y = 10000 i = p∙r∙t For one year, i = pr (pr) 6% + (pr) 8% = Total Interest x(.06)+ y(.08) = 760.06x +.08y = 760

19. REVIEW Teresa invested $10,000, part at 6% annual interest and the rest at 8% annual interest. If she received $760 in total simple interest at the end of the year, how much did she invest at each rate? x = inv. at 6% y = inv. at 8% x + y = 10000.06x +.08y = 760 [100] To eliminate decimals, multiply bottom equation by 100. 6x + 8y = 76000 x + y = 10000

20. REVIEW Teresa invested $10,000, part at 6% annual interest and the rest at 8% annual interest. If she received $760 in total simple interest at the end of the year, how much did she invest at each rate? x = inv. at 6% y = inv. at 8% x + y = 10000.06x +.08y = 760 [100] Multiply bottom equation by -6 6x + 8y = 76000 x + y = 10000 [-6]

21. REVIEW Teresa invested $10,000, part at 6% annual interest and the rest at 8% annual interest. If she received $760 in total simple interest at the end of the year, how much did she invest at each rate? x = inv. at 6% y = inv. at 8% x + y = 10000.06x +.08y = 760 [100] 6x + 8y = 76000 x + y = 10000 [-6] 6x + 8y = 76000 -6x – 6y = -60000 2y = 16000 y = 8000 x = 2000 $2000 at 6% $8000 at 8%