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Solving Linear Equations with Two Variables: Graphical, Substitution, and Elimination Methods

Learn how to solve systems of linear equations with two variables using graphical, substitution, and elimination methods, and apply these methods to solve real-life application problems.

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Solving Linear Equations with Two Variables: Graphical, Substitution, and Elimination Methods

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  1. Section 4.1 Systems With Two Variables

  2. The graphical method. A OBJECTIVES Find solution of two linear equations using:

  3. The substitution method. B OBJECTIVES Find solution of two linear equations using:

  4. The elimination method. C OBJECTIVES Find solution of two linear equations using:

  5. Solve applications involving systems of equations. D OBJECTIVES Find solution of two linear equations using:

  6. Solving Two Equations in Two Unknowns by Elimination Clear any fractions or decimals.

  7. Solving Two Equations in Two Unknowns by Elimination 2. Multiply both sides of the equations (as needed) by numbers that make the coefficients of one of the variables additive inverses.

  8. Solving Two Equations in Two Unknowns by Elimination 3. Add the two equations. 4. Solve for the remaining variable.

  9. Solving Two Equations in Two Unknowns by Elimination 5. Substitute this solution into one of the equations and solve for second variable. 6. Check the solution.

  10. Practice Test Chapter 4Systems With Two VariablesSection 4.1A Exercise #2

  11. Use the graphical method to solve the system.

  12. Use the graphical method to solve the system.

  13. Use the graphical method to solve the system. There is no solution. System is inconsistent. Lines are parallel.

  14. Use the graphical method to solve the system. 5 x -5 5 y -5

  15. Chapter 4Systems With Two VariablesSection 4.1A Practice Test Exercise #3

  16. Use the graphical method to solve the system. y x 5 -5

  17. Use the graphical method to solve the system. Infinitely many solutions y x 5 -5

  18. Practice Test Chapter 4Systems With Two Variables Section 4.1B Exercise #5

  19. Use the substitution method to solve the system.

  20. Use the substitution method to solve the system. NO solution

  21. Practice Test Chapter 4Systems With Two VariablesSection 4.1C Exercise #9

  22. Solve the system. Multiply by 6. Multiply by 8. Multiply by –2.

  23. Solve the system.

  24. Solve the system. Substitute x = 4 in

  25. Solve the system.

  26. Solve the system. Solution is (4, 0).

  27. Section 4.2 Systems with Three Variables

  28. Solve a system of three equations and three unknowns by the elimination method. A OBJECTIVES

  29. Determine if a system of three equations in three unknowns is consistent, inconsistent, or dependent. B OBJECTIVES

  30. Solve applications involving systems of three equations. C OBJECTIVES

  31. PROCEDURE FOR SOLVING Three Equations in Three Unknowns by Elimination Select a pair of equations and eliminate one variable from this pair.

  32. PROCEDURE FOR SOLVING Three Equations in Three Unknowns by Elimination 2. Select a different pair of equations and eliminate the same variable as in step 1.

  33. PROCEDURE FOR SOLVING Three Equations in Three Unknowns by Elimination 3. Solve the pair of equations resulting from step 1 and 2.

  34. PROCEDURE FOR SOLVING Three Equations in Three Unknowns by Elimination 4. Substitute the values found in the simplest of original equations. Solve for third variable.

  35. PROCEDURE FOR SOLVING Three Equations in Three Unknowns by Elimination 5. Check by substituting the values in each of the original equations.

  36. Solving Three Equations in Three Unknowns by Elimination The system is consistent & independent; it has one solution consisting of an ordered triple (x, y, z).

  37. Solving Three Equations in Three Unknowns by Elimination The system is inconsistent. It has no solution.

  38. Solving Three Equations in Three Unknowns by Elimination The system is consistent and dependent. It has infinitely many solutions.

  39. Practice Test Chapter 4Systems With Two VariablesSection 4.2A Exercise #11

  40. Solve the system. x = 1

  41. Solve the system. x = 1

  42. Solve the system. x = 1

  43. Section 4.3 Coin, Distance-Rate-Time, Investment and Geometry Problems

  44. Solve coin problems with two or more unknowns. A OBJECTIVES

  45. Solve general problems with two or more unknowns. B OBJECTIVES

  46. Solve rate, time and distance problems with two or more unknowns. C OBJECTIVES

  47. Solve investment problems with two or more unknowns. D OBJECTIVES

  48. Solve geometry problems with two or more unknowns. E OBJECTIVES

  49. Practice Test Chapter 4Systems With Two VariablesSection 4.3C Exercise #16

  50. A motorboat can go 10 mi downstream on a river in 20 min. It takes 30 min for this boat to go back upstream the same 10 mi. Find the speed of the current.

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