A 6-1

Find the POI of y = 12x +3 and y = −2x +8 by… Write the equation given the story.

…graphing.

…using Algebra. a) I start with 3$ and earn .5$ every week b) I start with 8$ and lose 2$ every week. c) I start with 50$ and earn 125$ each week. d) I start with 1050$ but lose 75$ each week.

A 6-1 Name ___________________________________BDFM?________Why?______________________________ 1. Find the POI 7−= xy and 53 +−= xy by… 2. Find the POI of 34 −= xy and 4+−= xy by… …graphing. POI ________

…graphing. POI ________

…using Algebra

…using Algebra.

Solution____________. Solution____________. 3. Alejandro starts with 50$ and earns 125$ a week. Angelina starts with 1050$ but loses 75$ a week. When will they have the same amount of money? Alejandro’s equation__________________________. Angelina’s equation___________________________.

4. Find the POI of

€

y = 3x − 5 and

€

y = −12x + 2 by… 5. Find the POI of

€

y = −32x + 5 and

€

y = x − 5 by…

…graphing. POI ________

…graphing. POI________

…using Algebra

…using Algebra.

Solution____________. Solution____________. 6. My son and daughter started a savings account on the same day. My son started with $20 and adds to his account (deposits) $10 every month. My daughter started with $110, but only deposits $7 each month. How many months will it take before my son has saved as much as my daughter? Write two equations and find the solution using algebra.

Son’s equation : ______________________ Daughter’s equation: ___________________________

A 6-2 1. Find the POI.

€

y = 2x +15x + 5y = 35

This system is gross because ______________________ ______________________!

€

y = 2x +15x + 5y = 35

This system is nice because ______________________ ______________________!

€

y = 2x +1

5x + 5(y) = 35

Before substitution.

€

y = 2x +15x + 5(y) = 35

After substitution.

€

y = 2x +15x + 5(2x +1) = 35

Find the POI.

€

y = 2x +1

5x + 5y = 35

A 6-2 Name____________________________________BDFM?__________Why?____________________________ Substitute but do not solve.

1. y = 5x2y+3x =1

2. y = 67y+ 4x = 9

3.

€

y = 8x + 42x − 9y =1

4. 2x + y = 8x = 2y+1

5. x = 2y+14y− 9x = 7

Find the POI. Thx.

6. y = x + 24y+3x = 36

(4, 6)

7. y = 2x + 55y+3x = 51

(4, 9)

8. y = x +32x +3y =19

(2, 5)

9. y = 4x −12x +3y = 25

(2, 7)

10. x = 2y+13x + y =17

(5, 2)

11. y = 3x +110x − 2y =18

(5, 16)

12. Find the POI by graphing. y = 2x −3y = −x + 9 POI:

y = 2x + 4y = 2x −3

POI:

y = 2x + 5y = 2x + 5

POI:

A 6-3 Elimination Find the POI.

1. 24841224

−=+

−=−−

yxyx

2.

€

x − y =112x + y =19

3.

€

−4x + 9y = 9x − 3y = −6

A 6-3 Name____________________________________BDFM?______Why?________________________________

1.

€

4x + 8y = 20−4x + 2y = −30

2. 925123

=+

−=−

yxyx

3. 624

1134−=+−

=+

xyxy

4. 6421042−=−

=+

yxyx

5.

€

−7x + y = −19−2x + 3y = −19

6.

€

−2x − 9y = −25−4x − 9y = −23

Find the POI.

7. 3

2+−=

=

xyxy

8. 732

1=+

+=

xyxy

9. 2x +3y = 84x −3y = −2

Which method?

Which method? Which method?

Graph to find the POI.

10. y = x + 9y = −2x −3

POI:

11. y = − 1

2x +8

y = 32x −8

POI:

12. y = 1

3x + 9

y = −2x − 5

POI:

A 6-Review Name____________________________________BDFM?__________Why?_________________________ Solve for x. 1) -4x = 29 2) 7x – 8 = 62 3) 6x – 7 = 3x + 11

4) Solve each system using any method. Be sure to show all your work!

a) 294312=+

−=

yxxy

Solution (______, ______) b) 54193+−=

+=

xyxy

Solution (______, ______)

c) 68232

=+

=+−

yxyx Solution (______, ______) d)

18541232

=+

−=−−

yxyx

Solution (______, ______)

5) Graph. y = x + 5

y-intercept slope

y = 2x + 4

y-intercept slope

y = 32x −1

y-intercept slope

6) Graph the system of equations below and find the point of intersection.

2

21

32

−=

+−=

xy

xy

Point of Intersection___________________ 7) Find the standard and/or factored form Factored form: (x + 5)(x + 2)

FF: 2(3x + 9)

FF:

FF:

FF:

2x −12

x2 −6x

−4x 32

x2 8x

Standard form:

SF: SF: SF: SF: