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REVIEW

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. REVIEW. 1. Solve by graphing: x – 2y = -3

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REVIEW

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

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

  4. REVIEW x – 2y = -3 y = -3x + 5 1. Solve by graphing: x – 2y = -3 y = -3x + 5 x – 2y = -3 3x + y = 5 [2] 2. Solve using substitution: x – 2y = -3 y = -3x + 5 x – 2y = -3 6x + 2y = 10 7x = 7 3. Solve using elimination: x – 2y = -3 y = -3x + 5 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. u = units digit = tens digit t more than

  6. REVIEW exceeds 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. The units digit twice the tens digit by 1. u = units digit = tens digit t

  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. u = units digit = tens digit t is 1 more than exceeds The units digit twice the tens digit by 1. twice the tens digit = 2 • t u + 1 u = 2t + 1

  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. u = units digit = tens digit t u = 2t + 1 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. sum of its digits is 10. u = units digit = tens digit t u = 2t + 1 sum of its digits is 10. of its digits is 10. sum

  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. u = units digit = tens digit t u = 2t + 1 of its digits is 10. sum 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. u = units digit = tens digit 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. u = units digit = tens digit t u = 2t + 1 u + t = 10 SUBSTITUTION 2t + 1 + t = 10 ADD LIKE TERMS 3t + 1 = 10 SUBT. PROP. OF EQ. 3t = 9 DIV. PROP. OF EQ. t = 3

  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. u = 2(3) + 1 u = units digit = tens digit t u = 6 + 1 u = 7 u = 2t + 1 u = 2t + 1 u + t = 10 SUBSTITUTION 2t + 1 + t = 10 ADD LIKE TERMS 3t + 1 = 10 SUBT. PROP. OF EQ. 3t = 9 DIV. PROP. OF EQ. t = 3

  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. u = 2(3) + 1 u = units digit = tens digit t u = 6 + 1 u = 7 u = 2t + 1 u + t = 10 How do we write the answer? 2t + 1 + t = 10 37 3t + 1 = 10 3t = 9 t = 3

  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 = 10000 + y

  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 = 10000 + y 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? i = p•r•t x = inv. at 6% y = inv. at 8% For one year, i = pr (pr)6% + (pr)8% = Total Interest x + y = 10000 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? i = p∙r∙t x = inv. at 6% y = inv. at 8% For one year, i = pr (pr)6% + (pr)8% = Total Interest x + y = 10000 .06x + .08y = 760 x(.06) + y(.08) = 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? To eliminate decimals, multiply bottom equation by 100. x = inv. at 6% y = inv. at 8% x + y = 10000 x + y = 10000 .06x + .08y = 760 [100] 6x + 8y = 76000

  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? Multiply bottom equation by -6 x = inv. at 6% y = inv. at 8% x + y = 10000 .06x + .08y = 760 [100] 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? 6x + 8y = 76000 -6x – 6y = -60000 x = inv. at 6% y = inv. at 8% 2y = 16000 y = 8000 x + y = 10000 x = 2000 .06x + .08y = 760 [100] $2000 at 6% $8000 at 8% 6x + 8y = 76000 x + y = 10000 [-6]

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