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Do Now 1/15/10. Copy HW in your planner. Text p. 462, #1-8 all, #10, #12, #16-30 evens, #36 Be ready to finish quiz sections 7.1 – 7.4. You will have 10 minutes. Objective. SWBAT identify the number of solutions of a linear system. “How Do You Solve a Linear System???”.

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do now 1 15 10
Do Now 1/15/10
  • Copy HW in your planner.
    • Text p. 462, #1-8 all, #10, #12, #16-30 evens, #36
  • Be ready to finish quiz sections 7.1 – 7.4. You will have 10 minutes.
objective
Objective
  • SWBAT identify the number of solutions of a linear system
how do you solve a linear system
“How Do You Solve a Linear System???”

(1) Solve Linear Systems by Graphing (7.1)

(2) Solve Linear Systems by Substitution (7.2)

(3) Solve Linear Systems by ELIMINATION!!! (7.3)

Adding or Subtracting

(4) Solve Linear Systems by Multiplying First (7.4)

Then eliminate.

section 7 5 solve special types of linear systems
Section 7.5 “Solve Special Types of Linear Systems”

LINEAR SYSTEM-

consists of two or more linear equations in the same variables.

Types of solutions:

(1) a single point of intersection – intersecting lines

(2) no solution – parallel lines

(3) infinitely many solutions– when two equations represent the same line

slide5

“Solve Linear Systems by Elimination” Multiplying First!!”

Multiply

First

Eliminated

x (2)

4x + 5y = 35

8x + 10y = 70

Equation 1

+

x (-5)

15x - 10y = 45

-3x + 2y = -9

Equation 2

23x = 115

“Consistent Independent

System”

x = 5

4x + 5y = 35

Equation 1

Substitute value for

x into either of the original equations

4(5) + 5y = 35

20 + 5y = 35

y = 3

4(5) + 5(3) = 35

35 = 35

-3(5) + 2(3) = -9

-9 = -9

The solution is the point (5,3).

Substitute (5,3) into both equations to check.

slide6

“Solve Linear Systems with No Solution”

Eliminated

Eliminated

3x + 2y = 10

Equation 1

_

+

-3x + (-2y) = -2

3x + 2y = 2

Equation 2

This is a false statement,

therefore the system has no

solution.

0 = 8

“Inconsistent

System”

No Solution

By looking at the graph, the lines

are PARALLEL and therefore will

never intersect.

slide7

“Solve Linear Systems with Infinitely Many Solutions”

x – 2y = -4

Equation 1

y = ½x + 2

Use ‘Substitution’ because we know what y is equals.

Equation 2

Equation 1

x – 2y = -4

x – 2(½x + 2) = -4

x – x – 4 = -4

This is a true statement,

therefore the system has infinitely many solutions.

-4 = -4

“Consistent

Dependent

System”

Infinitely Many Solutions

By looking at the graph, the lines are the SAME and therefore intersect at every point, INFINITELY!

slide8

“Tell Whether the System has No Solutions or Infinitely Many Solutions”

Eliminated

Eliminated

5x + 3y = 6

Equation 1

+

-5x - 3y = 3

Equation 2

This is a false statement,

therefore the system has no

solution.

“Inconsistent

System”

0 = 9

No Solution

slide9

“Tell Whether the System has No Solutions or Infinitely Many Solutions”

-6x + 3y = -12

Equation 1

y = 2x – 4

Use ‘Substitution’ because we know what y is equals.

Equation 2

Equation 1

-6x + 3y = -12

-6x + 3(2x – 4) = -12

-6x + 6x – 12 = -12

This is a true statement,

therefore the system has infinitely many solutions.

-12 = -12

“Consistent

Dependent

System”

Infinitely Many Solutions

how do you determine the number of solutions of a linear system
How Do You Determine the Number of Solutions of a Linear System?
  • First rewrite the equations in slope-intercept form.
  • Then compare the slope and y-intercepts.

y -intercept

slope

y = mx + b

identify the number of solutions
“Identify the Number of Solutions”
  • Without solving the linear system, tell whether the system has one solution, no solution, or infinitely many solutions.

5x + y = -2

-10x – 2y = 4

6x + 2y = 3

6x + 2y = -5

3x + y = -9

3x + 6y = -12

Infinitely many

solutions

No solution

One solution

y = -5x – 2

– 2y =10x + 4

y = -5x – 2

y = 3x + 3/2

y = 3x – 5/2

y = -3x – 9

y = -½x – 2

war identify the number of solutions
WAR!!“Identify the Number of Solutions”
  • Without solving the linear system, tell whether the system has one solution, no solution, or infinitely many solutions.
homework
Homework

NJASK7 Prep

  • Text p. 462, #1-8 all, #10, #12, #16-30 evens, #36