1. Systems of Equations Draw 2 lines on a piece of paper. There are three possible outcomes.

2. Outcome #1

3. Outcome #2

4. Outcome #3

5. Systems of Equations Two linear equations with the same two variables form a system of equations. A solution of the system is an ordered pair that makes both equations true. There are 3 outcomes.

6. Outcome #1 These lines intersect in a single point, so there is 1 solution.

7. Outcome #2 Since the lines do not touch, there is no solution.

8. Outcome #3

9. Solve each system by graphing. 1)y = -2x + 1 y = -3x + 4 2) y = 1/2x + 3 2y = x - 2 3) 4x + 2y = 8 3y = -6x + 12

10. Systems of Equations-Substitution Method 1) Solve 1 of the equations for 1 variable 2) Substitute that expression in the other equation and solve 3) Substitute that value in one of the original equations and solve 4) Check the solution in both equations

11. Examples Use substitution to solve each system. 1) y = 2 3x + 2y = 1 2) x + 2y = 2 3x - y = 6

12. Examples Use substitution to solve each system. 3) x + y = 4 2x - y = 5 4) x + 2y = 2 3x - y = 6

13. Systems of Equations- Elimination/Addition/Linear Combination Steps to follow: 1) Once the coefficients of one of the variables are opposites, add the 2 equations 2) Solve the resulting equation for the remaining value 3) Substitute that value in one of the original equations and solve 4) Check the solution in both equations

14. Examples Use elimination to solve each system. 1)x + y = 8 x – y = 2 2)2x + 7y = -5 -5x +7y = -12 3) 3x - 4y = 10 3y = 2x - 7