Essential Questions: When and how do you solve a system of equations using the substitution method? When and how do you solve a system of equations using the elimination method? Students will write a summary explaining when to use each method and the steps for using each method. Solving Systems of equations by graphing, substitution and elimination (Section 7-1 and 7-2)

Essential Questions: When and how do you solve a system of equations using the substitution method? When and how do you solve a system of equations using the elimination method? Students will write a summary explaining when to use each method and the steps for using each method. Solutions of a System of Equations  A solution to a system of equations is an order pair that gives true results when plugged into both equations.  If one equation is a multiple of the other (ex: y = x+1 and 3y = 3 x + 3) then there are infinitely many solutions.  It is possible for the system to have no solution (ex: you solve get to where x 2 – x + 1 = 0 which has no real solution.)

Essential Questions: When and how do you solve a system of equations using the substitution method? When and how do you solve a system of equations using the elimination method? Students will write a summary explaining when to use each method and the steps for using each method.

Essential Questions: When and how do you solve a system of equations using the substitution method? When and how do you solve a system of equations using the elimination method? Students will write a summary explaining when to use each method and the steps for using each method. Solve by Graphing Graph each line, the point where the line intersect is the solution.

Essential Questions: When and how do you solve a system of equations using the substitution method? When and how do you solve a system of equations using the elimination method? Students will write a summary explaining when to use each method and the steps for using each method. Example 1: Solve by graphing. x +y = 4 x – y = 2

Essential Questions: When and how do you solve a system of equations using the substitution method? When and how do you solve a system of equations using the elimination method? Students will write a summary explaining when to use each method and the steps for using each method. Solve by Substitution 1 ) Solve one equation for one variable. (ie get one of the equations to be x = or y =.) 2) Plug this into the other equation. 3) Solve for the variable. 4) Substitute the value you get into one of the equations and solve. Use Substitution when… The coefficient in front of x OR y is 1

Essential Questions: When and how do you solve a system of equations using the substitution method? When and how do you solve a system of equations using the elimination method? Students will write a summary explaining when to use each method and the steps for using each method. Example 2: Solve by substitution. x + y = 1 5x – 4y = -23

Essential Questions: When and how do you solve a system of equations using the substitution method? When and how do you solve a system of equations using the elimination method? Students will write a summary explaining when to use each method and the steps for using each method. Example 3: Solve by substitution. 6x – 3y – 4 = 0 x + 2y – 4 = 0

Essential Questions: When and how do you solve a system of equations using the substitution method? When and how do you solve a system of equations using the elimination method? Students will write a summary explaining when to use each method and the steps for using each method. x +y = 4 Example 4: Solve by substitution. x – y = 2

Essential Questions: When and how do you solve a system of equations using the substitution method? When and how do you solve a system of equations using the elimination method? Students will write a summary explaining when to use each method and the steps for using each method. Steps to use elimination: 1) Make sure x and y are lined up. 2) Find a coefficient to cancel. You may need to multiply by a constant first. Sometimes you need to multiply both equations. 3) Add two equations. Elimination is used when… Coefficients can easily be canceled! Cross out step 2 in notes!

Essential Questions: When and how do you solve a system of equations using the substitution method? When and how do you solve a system of equations using the elimination method? Students will write a summary explaining when to use each method and the steps for using each method. Example 4: Solve by elimination. 3x + 2y = 4 5x – 2y = 8

Essential Questions: When and how do you solve a system of equations using the substitution method? When and how do you solve a system of equations using the elimination method? Students will write a summary explaining when to use each method and the steps for using each method. Example 5: Solve by elimination. 5x + 3y = 9 2x – 4y = 14

Essential Questions: When and how do you solve a system of equations using the substitution method? When and how do you solve a system of equations using the elimination method? Students will write a summary explaining when to use each method and the steps for using each method. Example 6 Match each system of linear equations with its graph. Describe the number of solutions. Then state whether the system is consistent or inconsistent.

Essential Questions: When and how do you solve a system of equations using the substitution method? When and how do you solve a system of equations using the elimination method? Students will write a summary explaining when to use each method and the steps for using each method. HW #36 pg 481 (1-9 odd, 13, 15, 19) and HW #37 pg (7-13 odd, 17-20all, odd)