1. UNIT 2 – Linear Functions
Section 3 – Systems of Equations

2. ELIMINATION METHOD Supplemental Page 23: 2 (7x + 5y = 13)
Multiply by 2 and -7 to make the x coefficients be 14 and -14

3. ELIMINATION METHOD Supplemental Page 23:
2 (7x + 5y = 13) x + 10y = 26
-7 (2x + 3y = -1)  x – 21y = 7
-11y = 33
(Add down to cancel x)
y = -3

4. ELIMINATION METHOD Supplemental Page 23: 2x + 3(-3) = -1 2x – 9 = - 1
Solution: (4, -3)

5. ELIMINATION METHOD Supplemental Page 23: Practice: 5x + 6y = 35
3 (3x – 2y = -14) Multiply by 3 to cancel y
9x – 6y = * Combine w/ other eq.
14x = 21
x = 1.5

6. ELIMINATION METHOD Supplemental Page 23:
Practice: 5(1.5) + 6y = *If x = 1.5
y = 35
6y = 27.5
y =
(1.5, 4.583)

7. SUBSTITUTION METHOD Example: 3x +7y = 83 and y = 4x+3
i) Since y = 4x + 3, substitute 4x+3 in for y
3x + 7(4x+3) = 83
ii) Solve 3x + 28x + 21 = 83
31x + 21 = 83
31x = 62
x = 2

8. SUBSTITUTION METHOD Example: x = 2 iii) y = 4(2) + 3 = 11
iv) Solution is (2, 11)

9. SUBSTITUTION METHOD Practice: 3x – 6(2x + 4) = 12 3x – 12x – 24 = 12
y = 2(-4) + 4 = Solution (-4, -4)

10. Graph Linear Inequalities
SUPPLEMENTAL PACKET p. 24
1) y > 4x – 3 and y > -2x + 3
Graph each line using y-intercept and slope.
The first line is dashed, second is solid.
The solution is the area of points that fit BOTH graphs.
It must be above (>) both lines.

11. Graph Linear Inequalities
1) y > 4x – 3 and y > -2x + 3
It must be above (>) both lines.

12. Graph Linear Inequalities
3) y < 3 and y < -x + 1
Remember y = 3 is a horizontal line through 3
It must be below (<) both lines.
PRIZM – Enter Y1: 3 and Y2: -x+1
CONVERT each
Use F5 GSOLV
for key points

13. Graph Linear Inequalities
5) x < -3 and 5x + 3y > -9
Remember x = -3 is a vertical line through -3
5x + 3y > -9 must be rewritten in y=mx+b
3y > -5x – 9
y > -5/3 x - 3

14. Graph Linear Inequalities
5) x < -3
y > -5/3 x – 3
Below the first line (Left because it is x = )
Above the second line
Use PRIZM to confirm

15. Graph Linear Inequalities
PRACTICE: Supplemental packet p. 24, 25: 2, 8
Assignment: Supplemental packet p. 24, 25: 4, 6, 7

16. Word Problems Supplemental packet p. 26: 1 Given: State variables:
145 total points, 2 point questions and 5 point questions
50 total questions, 2 types of questions.
State variables:
x = Number of two point questions
y = Number of five point questions

17. Word Problems System: ________ + ________ = 145 (Number of points)
________ + ________ = 50 (Number of questions)
2x + 5y = 145
x + y = 50

18. Word Problems Solve: 2x + 5y = 145 2x + 5y = 145
2x + 5(15) =  x + 75 =  x = 35
(15, 35) two point and 35 five point questions

19. Word Problems 2) System: ________ + ________ = 2200 (Total people)
________ + ________ = (Total money brought in)
x + y = 2200
1.5x + 4y = 5050

20. Word Problems 2) Solve: x + y = 2200 1.5x + 4y = 5050
PRIZM – Go to the Equation App (A). Use F1 Simultaneous
F1 for 2 unknowns
Enter coefficients – EXE
x = 1500, y = 700
1500 children, 700 adults

21. Word Problems 3) Given: System:
90,000 debt is a starting value plus $2 for each (slope)
$17 profit each (slope)
System:
y = 2x
y = 17x

22. Word Problems y = 2x + 90000 y = 17x 17x = 2x + 90000
They will break even when they sell 6000 products

23. Word Problems PRACTICE: Supplemental Packet p. 27
ASSIGNMENT: Supplemental Packet p. 28

24. Systems in 3 variables Supplemental Packet p. 29
Read p. 154: Example 2 to fill in each part
Practice: Supplemental Packet p. 30
Assignment: Supplemental Packet p. 31

25. Systems in 3 variables
Supplemental Packet p. 30