UNIT 2 – Linear Functions Section 3 – Systems of Equations

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

ELIMINATION METHOD Supplemental Page 23: 2 (7x + 5y = 13) 14x + 10y = 26 -7 (2x + 3y = -1)  -14x – 21y = 7 -11y = 33 (Add down to cancel x) y = -3

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

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

ELIMINATION METHOD Supplemental Page 23: Practice: 5(1.5) + 6y = 35 *If x = 1.5 7.5 + 6y = 35 6y = 27.5 y = 4.5833333 (1.5, 4.583)

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

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

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

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.

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

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

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

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

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

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

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

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

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

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

Word Problems 3) Given: System: 90,000 debt is a starting value plus $2 for each (slope) $17 profit each (slope) System: y = 2x + 90000 y = 17x

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

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

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

Systems in 3 variables Supplemental Packet p. 30