Warm Up 1)Find the 43 rd term of the sequence 47, 34, 21, 8, …. 2)Rewrite in slope-intercept form -5y + 3x = -9.

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Presentation transcript:

Warm Up 1)Find the 43 rd term of the sequence 47, 34, 21, 8, …. 2)Rewrite in slope-intercept form -5y + 3x = -9

Homework Check Page 2 1a) t = 14c – 4b) $80 3a) c =.02n +.30b) 740 minutes Page 3 1)a)4.29x y = 30b) 5.1 pounds 4) a) 2x + 5y = 150b) (0,30) (75,0) (50,10)

Homework Check 2.2 (Page 4) 1)y = 4/3x – 82) y = 1/2x – 7 3) a)2b) 3c) 1 d) 4 4) a) y =.75x + 3b) $9c) 16 miles 5) a) 2W + 1T = 20b) 6 tie games

Systems of Equations

OBJECTIVES To understand what a system of equations is. Be able to solve a system of equations from graphing, substitution, or elimination Determine whether the system has one solution, no solution, or an infinite amount of solutions.

Defining a System of Equations A system of equations is a grouping of 2 or more equations, containing one or more variables. Examples: x + y = 2 2x + y = 5 2y = x + 2 y = 5x - 7 6x - y = 5

Solution? To be a solution to the system, all equations must be satisfied. Is (-3, 4) a solution to the system?

Types of Solutions Intersecting Lines have ONE unique solution. Coincidental Lines (or same lines) have infinitely MANY solutions. Parallel Lines have NO solutions!

Solving Systems of Equations There are three methods to solving a system of equations 1.Graphing 2.Substitution 3.Elimination

Graphing

Graphing Calculator Step 1: Step 2: Step 3: Step 4:

Examples… 1) Determine whether the following have one, none, or infinitely many solutions 2y + x = 8 y = 2x + 4 3)2) x - 5y = 10 -5y = -x +6 y = -6x + 8 y + 6x = 8 ANS: One Solution ANS: No Solution ANS: Infinite Solutions

Solving Systems by Substitution

Solving by Substitution Steps If one of the equations is already solved for a variable, Substitution may be an easy method to solve. Step 1: Make sure one of the equations is solved for a variable. Step 2: Substitute the expression into the other equation. Step 3: Solve for the variable. Step 4: Substitute the value of x (or y) into either equation and solve.

Example Solve the system by substitution.

Solving Systems by Elimination

Elimination We can solve by elimination by either Adding or Subtracting two equations to eliminate a variable!

Example Solve by Elimination

Example Solve by Elimination

More with Elimination If one will not cancel, multiply one or both equations to get variables to cancel

Example Solve the system by elimination.

Special Solutions Solve each system by elimination. 1.2.

Homework