Systems of Equations and Inequalities in Two Variables A-REI.3; A-REI.5; A-REI.6; A-REI.7.

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Systems of Equations and Inequalities in Two Variables A-REI.3; A-REI.5; A- REI.6; A-REI.7

Transcript of Systems of Equations and Inequalities in Two Variables A-REI.3; A-REI.5; A-REI.6; A-REI.7.

Systems of Equations and Inequalities in Two Variables

A-REI.3; A-REI.5; A-REI.6; A-REI.7

EQ: How Do Solve Systems of Equations with the Graphing Method?

04/19/23

System of Equations

A collection of 2 or more lines, including nonlinear equations

Solution to a system

The ordered pair (or set of points) that satisfy all equations in the system, at the same time

Called the point of intersection

There are three different types: no solution, infinite solutions, one solution

One Solution

The two lines cross each other in exactly one point on the graph

Infinite Solutions

The two lines on the graph lie on top of each other.

No Solution

The two lines never cross.a = b

x = a

a = a

Example 1: Find the solution to given system:

y = -1x +3

y = 1x – 3 2

Solution: (4, -1)

Guided Practice 1Find the solution to given system:

y = 2x – 5 y = -3x + 2 2

Solution:

(2, -1)

Guided Practice 2Find the solution to given system:

y = – 5 y = -4x + 3

Solution:

(2, -5)

Guided Practice 3Find the solution to given system:

y = 2x – 6 y = 1x + 2 4

Solution:

(4, -3)

QuestionsHow many times do the lines cross in order to have one solution?

What does having a solution mean?

What does every line need to have when drawn?

Example 2: Find the solution to given system:

y = 2x + 4

y = 6x 3

Solution: No Solution

Guided Practice 4Find the solution to given system:

x – y = 4-5x + 5y = -20

x – y = 4-x -x -y = -x + 4__

-1__-1

__-1

y = x - 4

-5x + 5y = -20+5x +5x____________

5y = 5x – 20 __ 5

__ 5

__ 5

y = x – 4

y = x - 4 y = x – 4

Solution:Infinite Solutions

Guided Practice 5Find the solution to given system:

-4x + 8y = 16 6x – 3y = 12

-4x + 8y = 16+ 4x + 4x______________ 8y = 4x + 16__

8__ 8

__ 8

y = 1x + 2 2

y = 1x + 2 2

-6x -6x____________-3y = -6x + 12__-3

__-3

__-3

y = 2x – 4

y = -2x – 4

Solution:(4, 4)

QuestionsWhat variable do you need to solve for in order to graph?

What will be the same in equations that have no solution?

What will be the same in equations that have infinite solutions?