Warm – Up #3

Graph the following: 1. y = 2x – 1 2. y = - 3x + 3

Practice/Review

Graphing #1

1. y = 2

2. x = - 3

Graphing #2

1.x – intercept: 52.y – intercept: -4

Graphing #3

1.2x + 3y = 12

Graphing #4

1.y = - 5 2.x = 1

Graphing #5

1. x – intercept: - 3 2. y – intercept: 6

Graphing #6

1. - 4x + 6y = 36

Question?

Describe what you think the word independent and dependent means. (Does not have to relate to math).

Day 3 Block Unit Question:

How do I justify and solve the solution to a system of equations or inequalities?

Standard: MCC9-12.A.REI.1, 3, 5, 6, and 12

I can…

Graph systems of equations and identify their solutions

Solve Systems of Equations by

Graphing

Tri-fold Activity! Everyone gets one piece of colored

paper. Fold it hot dog style Cut three slits in your paper. It should look like this!

Tri-fold Activity! Title your foldable.

o System of Equations Label each flap.

o Intersecting lineso Parallel lines o Same Line

On the back of your Tri-fold title a section for “Steps.”

Save some room for pictures!

Steps1. Make sure each equation is

in slope-intercept form: y = mx + b.

2. Graph each equation on the same graph paper.

3. The point where the lines intersect is the solution. If they don’t intersect then there’s no solution.

4. Check your solution algebraically.

Types of Systems There are 3 different types of

systems of linear equations

3 Different Systems:1) One solution2) No Solution3) Infinite Solutions

What type of Solution?

Solution: Infinitely Many

32

32

xy

xy

Type 1: Consistent-dependent

A system of linear equations having an infinite number of solutions is described as being consistent-dependent.

y

x

The system has infinite solutions, the lines are identical

2 5

2 1

y x

y x

No Solution

What type of Solution?

Type 2: Inconsistent A system of linear equations having no

solutions is described as being inconsistent.

y

x

The system has no solution, the lines are parallelRemember, parallel lines have the same slope

y = 3x – 12

y = -2x + 3

What type of Solution?

Solution: (3, -3)

Type 3: Consistent-independent

A system of linear equations having exactly one solution is described as being one solution.y

x

The system has exactly one solution at the point of intersection

So basically…. If the lines have the same y-intercept b,

and the same slope m, then the system is consistent-dependent

If the lines have the same slope m, but different y-intercepts b, the system is inconsistent

If the lines have different slopes m, the system is consistent-independent

More Examples:

The ordered pair (5, 9) is a solution of which linear system?

A. B.

2

2 3 9

x y

x y

Solution: (-3, 1)

Graph to find the solution.

Solution: (-2, 5)

Graph to find the solution.

5

2 1

y

x y

2

2 3 9

x y

x y

Solution: (-3, 1)

3. Graph to find the solution.

Solution: (-2, 5)

4. Graph to find the solution.

5

2 1

y

x y

CWGraphing WS

HWHomework Packet

Warm – Up #4Graph the following system of equations:

1. y = -2x + 1 y = 3x + 5

Review Graphing System of Equations

Day 4 Block Unit Question:

How do I justify and solve the solution to a system of equations or inequalities?

Standard: MCC9-12.A.REI.1, 3, 5, 6, and 12

I can…

Solve systems of equations by substitution and elimination.

Solve Systems of Equations by Substitution

Steps1. One equation will have either x or y by

itself, or can be solved for x or y easily.2. Substitute the expression from Step 1 into

the other equation and solve for the other variable.

3. Substitute the value from Step 2 into the equation from Step 1 and solve.

4. Your solution is the ordered pair formed by x & y.

5. Check the solution in each of the original equations.

Warm – Up

Solve by Substitution:

1) 2x = 8 2) y = x – 4

x + y = 2 4x + y = 26

Steps for Elimination:

1. Arrange the equations with like terms in columns

2. Multiply, if necessary, to create opposite coefficients for one variable.

3. Add the equations.

4. Substitute the value to solve for the other variable.

5. Check

EXAMPLE 1

2 2 8

2 2 4

x y

x y

Example 1

EXAMPLE 2

4x + 3y = 16

2x – 3y = 8

Example 2

EXAMPLE 3

3x + 2y = 7

-3x + 4y = 5

Example 3

EXAMPLE 4

2x – 3y = 4

-4x + 5y = -8

Example 4

EXAMPLE 5

5x + 2y = 7

-4x + y = –16

Example 5

2x + 3y = 1

4x – 2y = 10

EXAMPLE 6Example 6

Warm – Up – Find the Error 1. 2.

Check this out!

All I Do Is Solve

By: Westerville South H.S.

CWSubstitution &

Elimination Practice

HWHomework Packet