Solving system by graphing
- 1. Holt McDougal Algebra 1 Solving Systems by SubstitutionSolving Systems by Substitution Holt Algebra 1 Warm UpWarm Up Lesson PresentationLesson Presentation Lesson QuizLesson Quiz Holt McDougal Algebra 1
- 2. Holt McDougal Algebra 1 Solving Systems by Substitution Warm Up Solve the linear equations for x. 1. y = x + 3 2. y = 3x – 4 Simplify each expression. x = y – 3 2x – 103. 2(x – 5) 4. 12 – 3(x + 1) 9 – 3x
- 3. Holt McDougal Algebra 1 Solving Systems by Substitution Warm Up Continued Evaluate each expression for the given value of x. 5. x + 8 for x = 6 6. 3(x – 7) for x =10 12 9
- 4. Holt McDougal Algebra 1 Solving Systems by Substitution Solve systems of linear equations in two variables by substitution. Objective
- 5. Holt McDougal Algebra 1 Solving Systems by Substitution Sometimes it is difficult to identify the exact solution to a system by graphing. In this case, you can use a method called substitution. The goal when using substitution is to reduce the system to one equation that has only one variable. Then you can solve this equation by the methods taught in Chapter 2.
- 6. Holt McDougal Algebra 1 Solving Systems by Substitution Solving Systems of Equations by Substitution Step 2 Step 3 Step 4 Step 5 Step 1 Pick one equation and solve for one variable. Circle this equation. Substitute the resulting expression into the other equation. Solve that equation to get the value of the first variable. Substitute this value back into the circled equation from Step 1. Write the values from steps 3 and 4 as an ordered pair, (x, y), and check.
- 7. Holt McDougal Algebra 1 Solving Systems by Substitution Solve the system by substitution. Example 1: y = x + 1 4x + y = 6
- 8. Holt McDougal Algebra 1 Solving Systems by Substitution Solve the system by substitution. Example 2: x + 2y = –1 x – y = 5
- 9. Holt McDougal Algebra 1 Solving Systems by Substitution Example 3: Solve the system by substitution. y – x = 3 y = 2x + 5
- 10. Holt McDougal Algebra 1 Solving Systems by Substitution Example 4: Solve the system by substitution. x = 2y – 4 x + 8y = 16
- 11. Holt McDougal Algebra 1 Solving Systems by Substitution Example 5: Solve the system by substitution. 2x + y = –4 x + y = –7
- 12. Holt McDougal Algebra 1 Solving Systems by Substitution Example 6: y + 6x = 11 3x + 2y = –5 Solve by substitution.
- 13. Holt McDougal Algebra 1 Solving Systems by Substitution Example 7: –2x + y = 8 3x + 2y = 9 Solve by substitution.
- 14. Holt McDougal Algebra 1 Solving Systems by Substitution Lesson Quiz: Part I Solve each system by substitution. 1. 2. 3. (1, 2) (–2, –4) y = 2x x = 6y – 11 3x – 2y = –1 –3x + y = –1 x – y = 4