Algebra IIAlgebra II

3.1: Solve Linear Systems by Graphing3.1: Solve Linear Systems by Graphing

HW: p.156 (4, 8, 10, 12), review old HW: p.156 (4, 8, 10, 12), review old graphing: absolute value, quadratics, etc.graphing: absolute value, quadratics, etc.

Test: Next week ThursdayTest: Next week Thursday

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

Graph both lines in the same coordinate Graph both lines in the same coordinate plane.plane.

Your solution is the ordered pair where Your solution is the ordered pair where the two lines intersect.the two lines intersect. What would be the solution if the lines What would be the solution if the lines

do not intersect?do not 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 = -3y = -3xx – 2 – 2

33xx + 2 + 2yy = 2 = 2

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

2.) y = 22.) y = 2

xx = -4 = -4

3.) 23.) 2xx + + yy = 4 = 4

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

4.) y = -14.) y = -1

33xx + y = 5 + y = 5

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

Algebra IIAlgebra II

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

HW: 164 (28-38 even)HW: 164 (28-38 even)

Test: Thursday, 4/2Test: Thursday, 4/2

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)

Solve the system using the Solve the system using the substitution method.substitution method.

22xx + 5 + 5yy = -5 = -5

xx + 3 + 3yy = 3 = 3

Solve the system using the Solve the system using the elimination method.elimination method.

33xx – 7y = 10 – 7y = 10

66xx – 8y = 8 – 8y = 8

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

3.) 3x – 6y = 93.) 3x – 6y = 9 4.) 12x – 3y = -94.) 12x – 3y = -9

-4x + 7y = -16 -4x + y = 3-4x + 7y = -16 -4x + y = 3

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

3.) 3x – 6y = 93.) 3x – 6y = 9 4.) 12x – 3y = -94.) 12x – 3y = -9

-4x + 7y = -16 -4x + y = 3-4x + 7y = -16 -4x + y = 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 are t-shirts. Short sleeve t-shirts cost $5 each and are

sold for $8 each. Long sleeve t-shirts cost the 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 and school spends a total of $2500 on t-shirts and

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

3.4: Solve the system.3.4: Solve the system.4x + 2y + 3z = 14x + 2y + 3z = 1

2x – 3y + 5z = -142x – 3y + 5z = -14

6x – y + 4z = -16x – y + 4z = -1