Find the solution to the Find the solution to the system graphically.system graphically.

y = -3y = -3xx + 2 + 2

y = 2y = 2xx – 3 – 3

Algebra IIAlgebra II3.1: Solve Linear Systems by Graphing3.1: Solve Linear Systems by Graphing

Practice (no hw): p.156 (3, 4, 8, 9, 11) Practice (no hw): p.156 (3, 4, 8, 9, 11)

Quiz 3.1-3.2: Wednesday – 11/6 Quiz 3.1-3.2: Wednesday – 11/6

How to solve linear systems How to solve linear systems graphically.graphically.

Graph both lines in the same coordinate plane.Graph both lines in the same coordinate plane. Your solution is the ordered pair where the two Your solution is the ordered pair where the two

lines intersect.lines intersect. What would be the solution if the lines do not What would be the solution if the lines do not

intersect?intersect? What would be the solution if the lines What would be the solution if the lines

overlap each other?overlap each other?

Find the solution to the Find the solution to the system graphically.system graphically.

y = 2y = 2

xx = -4 = -4

Find the solution to the Find the solution to the system graphically.system graphically.

y = -3y = -3xx – 2 – 2

33xx + 2 + 2yy = 2 = 2

Find the solution to the Find the solution to the system graphically.system graphically.

22xx + + yy = 4 = 4

-4-4xx - 2 - 2yy = -2 = -2

Find the solution to the Find the solution to the system graphically.system graphically.

y = -1y = -1

33xx + y = 5 + y = 5

Do Now: Find the solution to the Do Now: Find the solution to the system graphically.system graphically.

xx – 7y = 7 – 7y = 7

-3-3xx + 21y = -42 + 21y = -42

Algebra IIAlgebra II

3.2: Solve Linear Systems Algebraically3.2: Solve Linear Systems Algebraically

HW: p.164 (4-14 even)HW: p.164 (4-14 even)

Quiz 3.1, 3.2: Wednesday, 11/6Quiz 3.1, 3.2: Wednesday, 11/6

What are the two algebraic methods of What are the two algebraic methods of solving a system of equations? solving a system of equations?

SubstitutionSubstitution

Elimination (linear combinations)Elimination (linear combinations)

3.2 B: Solve the system using substitution3.2 B: Solve the system using substitution1.) x + 2y = 61.) x + 2y = 6

3x – 2y = 23x – 2y = 2

Solve the system using substitutionSolve the system using substitution2.) 6x – 2y = 52.) 6x – 2y = 5

-3x + y = 7-3x + y = 7

3.) x + 3y = 33.) x + 3y = 3

2x – 4y = 62x – 4y = 6

3.2 B: Solve the system using substitution3.2 B: Solve the system using substitution

p.162 Example 3p.162 Example 3

To raise money for uniforms, your school sells To raise money for uniforms, your school sells

t-shirts. Short sleeve t-shirts cost $5 each and t-shirts. Short sleeve t-shirts cost $5 each and

are sold for $8 each. Long sleeve t-shirts cost are sold for $8 each. Long sleeve t-shirts cost

the school $7 each and are sold for $12 each. the school $7 each and are sold for $12 each.

The school spends a total of $2500 on t-shirts The school spends a total of $2500 on t-shirts

and sells all of them for $4200. How many short and sells all of them for $4200. How many short

sleeve t-shirts are sold?sleeve t-shirts are sold?

p.165 # 55p.165 # 55

In one week, a music store sold 9 guitars for a In one week, a music store sold 9 guitars for a

total of $3611. Electric guitars sold for $479 each total of $3611. Electric guitars sold for $479 each

and acoustic guitars sold for $339 each. How and acoustic guitars sold for $339 each. How

many type of each guitar were sold?many type of each guitar were sold?

4.) 3x – y = 24.) 3x – y = 2

6x + 3y = 146x + 3y = 14

Solve the system using substitutionSolve the system using substitution

1.) -3x + 3y = 31.) -3x + 3y = 3

3x + y = 93x + y = 9

3.2 B: Solve the system using elimination3.2 B: Solve the system using elimination

2.) -5x + 12y = 202.) -5x + 12y = 20

x – 2y = -6x – 2y = -6

3.2 B: Solve the system using elimination3.2 B: Solve the system using elimination

Solve the system using the Solve the system using the substitution or elimination method.substitution or elimination method.

1.) 4x + 3y = -21.) 4x + 3y = -2 2.) 3x + 3y = -152.) 3x + 3y = -15

x + 5y = -9x + 5y = -9 5x – 9y = 3 5x – 9y = 3

Do Now: Solve the system using the Do Now: Solve the system using the elimination method.elimination method.

1.) 3x – 6y = 91.) 3x – 6y = 9

-4x + 7y = -16-4x + 7y = -16

Do Now: Solve the system using the Do Now: Solve the system using the substitution or elimination method.substitution or elimination method.

2.) 12x – 3y = -92.) 12x – 3y = -9

-4x + y = 3-4x + y = 3

Solve the system using any method.Solve the system using any method.

1.) 21.) 2xx + 5 + 5yy = -5 = -5

xx + 3 + 3yy = 3 = 32.) 32.) 3xx – 7y = 10 – 7y = 10

66xx – 8y = 8 – 8y = 8