Warm Up

1) Find the 43rd term of the sequence 47, 34, 21, 8, ….

2) Rewrite in slope-intercept form -5y + 3x = -9

Homework CheckPage 21a) t = 14c – 4 b) $803a) c = .02n + .30 b) 740 minutes

Page 31)a)4.29x + 3.99y = 30 b) 5.1 pounds4) a) 2x + 5y = 150 b) (0,30) (75,0)

(50,10)

Homework Check 2.2 (Page 4) 1) y = 4/3x – 8 2) y = 1/2x – 7

3) a)2 b) 3 c) 1 d) 4

4) a) y = .75x + 3 b) $9c) 16 miles

5) a) 2W + 1T = 20 b) 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 SolutionsIntersecting 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. Graphing2. Substitution3. Elimination

Graphing

Graphing CalculatorStep 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.

ExampleSolve 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