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p.123 #55

p.123 #55. SOLUTIONS p = independent, n = dependent b) n = -1600 p + 14,800 A: ($8, 2000 widgets) B: ($3, 10000 widgets) c) n = -6000 p + 32,000. 3.2 Solving Systems Algebraically. Solving Systems by Substitution. 1) Solving Systems by Substitution.

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p.123 #55

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  1. p.123 #55 SOLUTIONS • p = independent, n = dependent b) n = -1600p + 14,800 A: ($8, 2000 widgets) B: ($3, 10000 widgets) c) n = -6000p + 32,000

  2. 3.2 Solving Systems Algebraically Solving Systems by Substitution

  3. 1) Solving Systems by Substitution • Sometimes graphing a system of equations produces a solution that is difficult to interpret

  4. 1) Solving Systems by Substitution • Sometimes it’s easier to use algebra to solve a system of equations • How??

  5. 1) Solving Systems by Substitution Example 1: Solve the system by substitution. 4x + 3y = 4 2x – y = 7 {

  6. 1) Solving Systems by Substitution Example 1: Solve the system by substitution. 4x + 3y = 4 2x – y = 7 { Substitution – “sub” one equation into the other

  7. 1) Solving Systems by Substitution Example 1: Solve the system by substitution. 4x + 3y = 4 2x – y = 7 { Substitution – “sub” one equation into the other • Number the equations as 1 and 2 • Re-write one equation as x = OR y = • Sub one equation into the other. Solve for the unknown. • Sub the known value into the other equation. Solve for the remaining unknown.

  8. 1) Solving Systems by Substitution Example 1: Solve the system by substitution. 4x + 3y = 4 1 2x – y = 7 2 Step 1: Number the equations {

  9. 1) Solving Systems by Substitution Example 1: Solve the system by substitution. 4x + 3y = 4 1 2x – y = 7 2 Step 2: Re-write one of the equations as x= ORy=, whichever is easiest {

  10. 1) Solving Systems by Substitution Example 1: Solve the system by substitution. 4x + 3y = 4 1 2x – y = 7 2 2x – 7 = y y = 2x – 7 Step 2: Re-write one of the equations as x= ORy=, whichever is easiest {

  11. 1) Solving Systems by Substitution Example 1: Solve the system by substitution. 4x + 3y = 4 1 2x – y = 7 2 2x – 7 = y y = 2x – 7 Step 3: Sub y = 2x – 7into equation 1 . Solve for x. {

  12. 1) Solving Systems by Substitution Example 1: Solve the system by substitution. 4x + 3y = 4 1 4x + 3(2x– 7) = 4 Step 3: Sub y = 2x – 7into equation 1 . Solve for x. “y” becomes “2x – 7”

  13. 1) Solving Systems by Substitution Example 1: Solve the system by substitution. 4x + 3y = 4 1 4x + 3(2x– 7) = 4 4x + 6x – 21 = 4 10x = 21 + 4 10x = 25 x = 2.5 “y” becomes “2x – 7”

  14. 1) Solving Systems by Substitution Example 1: Solve the system by substitution. 4x + 3y = 4 1 4x + 3(2x– 7) = 4 4x + 6x – 21 = 4 10x = 21 + 4 10x = 25 x = 2.5 “y” becomes “2x – 7” Step 4: Sub x = 2.5into equation 2 . Solve fory.

  15. 1) Solving Systems by Substitution Example 1: Solve the system by substitution. y = 2x – 7 2 y = 2(2.5) – 7 y = -2 “x” becomes “2.5” Step 4: Sub x = 2.5into equation 2 . Solve fory.

  16. 1) Solving Systems by Substitution Example 1: Solve the system by substitution. Therefore, the solution is (2.5, -2).

  17. 1) Solving Systems by Substitution Example 2: Solve the system by substitution. Check your answer. x + 6y = 2 5x + 4y = 36 {

  18. 1 2 1) Solving Systems by Substitution Example 2: Solve the system by substitution. Check your answer. x + 6y = 2 x = 2 – 6y 5x + 4y = 36 1 {

  19. 1 1 2 2 1) Solving Systems by Substitution Example 2: Solve the system by substitution. Check your answer. x + 6y = 2 x = 2 – 6y Sub in 5x + 4y = 36 5(2– 6y) + 4y = 36 10 – 30y + 4y = 36 -26y = 26 y = -1 {

  20. 1 1 1 2 2 1) Solving Systems by Substitution Example 2: Solve the system by substitution. Check your answer. x + 6y = 2 x = 2 – 6y Sub in 5x + 4y = 36 5(2– 6y) + 4y = 36 10 – 30y + 4y = 36 -26y = 26 y = -1 Sub in {

  21. 1 2 1) Solving Systems by Substitution Example 2: Solve the system by substitution. Check your answer. x + 6y = 2 5x + 4y = 36 x = 2 – 6(-1) x = 8 {

  22. 1) Solving Systems by Substitution Example 2: Solve the system by substitution. Check your answer. x + 6y = 2 5x + 4y = 36 Therefore, the solution to the system is (8, -1). {

  23. 1) Solving Systems by Substitution Example 2: Solve the system by substitution. Check your answer. x + 6y = 2 5x + 4y = 36 Check: 8 + 6(-1) = 2 5(8) + 4(-1) = 36 2 = 2 36 = 36 {

  24. Homework p.128 #1-5, 13, 47, 48, 52 Tomorrow: Solving Systems by Elimination

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