1. even though he knows you are slightly cracked.” "A true friend is someone who thinks you are a good egg

2. Warm Up How many solutions to the system shown in each graph? x y x y x y (1) (2) (3) one solution no solution infinitely many solutions

3. 5-2A Solving Linear Systems by Substitution Algebra 1 Glencoe McGraw-HillLinda Stamper

4. Two or more linear equations in the same variable form a system of linear equations, or simply a linear system. x + y = 5 Equation 1 2x – 3y = 3 Equation 2 A solution of a linear system in two variables is an ordered pair that makes each equation a true statement. In the previous lesson you solved a linear system by using a graph.

5. The point where the graphs of each equation intersect is the ordered pair solution. Point of intersection (–1,–3) x y There are several ways to solve a linear system without using a graph. In this lesson you will study an algebraic method known as the substitution method.

6. 1) Choose one of the equations and isolate one of the variables. 2) Substitute the expression from Step 1 into the other equation and solve. 3) Substitute the solved variable from Step 2 into either of the original equations and solve. Write the answer as an ordered pair. 4) Check the ordered pair solution in each of the original equations. Solving A Linear System By Substitution

7. First choose one equation and isolate one of the variables. You will get the same solution whether you solve for x first or y first. You should begin by solving for the variable that is easier to isolate. Which of the above equations would be easier to isolate one of the variables? Here is a linear system:

8. Which equation would you choose to isolate the variable? Name the variable you would solve for first.

9. 1) Choose one of the equations and isolate one of the variables. 2) Substitute the expression from Step 1 into the other equation and solve. 3) Substitute the solved variable from Step 2 into either of the original equations and solve. Write the answer as an ordered pair. 4) Check the ordered pair solution in each of the original equations. Solving A Linear System By Substitution

10. Solve the linear system using the substitution method. Choose one equation and isolate one of the variables. Substitute the expression into the other equation and solve. Substitute the solved value into one of the original equations and solve. Write the answer as an ordered pair. Remember to place the x value first. (–1,0) Watch one more time on how to do this problem!

11. Solve the linear system using the substitution method. (–1,0)

12. Solve the linear system using substitution. Example 1 Example 2 Example 3

13. Example 1 Solve the linear system.

14. Example 2 Solve the linear system.

15. Example 3 Solve the linear system. (3,–4) Did you distribute the negative correctly?

16. Solve the linear system. Write in your notes: When solving produces a false statement, there is no solution. What would the graph of this system look like to show “no solution”? No solution

17. x y Parallel lines

18. Solve the linear system. Write in your notes: When solving produces a true statement, there are infinitely many solutions. What would the graph of this system look like to show “infinitely many solutions”? Infinitely many solutions

19. x y Same lines

20. Practice Problems. Use substitution to solve each system of equations. If the system does not have exactly one solution, state whether it has no solution or infinitely many solutions. If the system has one solution, name it. no solution Infinitely many solutions (1,2) Infinitely many solutions (2,1) no solution

21. 5-A3 Pages 263-265 #8–19,43–48.