1 HW: pgs. 256-257 #11-27odd, 28-31 Weeks Money Saved ($) 28. y = 5x + 25 28. y = 8x + 16 29.Answer: 3 weeks 1 2 3 4 5 30. y = 15x + 10 28. y = -20x +

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1 HW: pgs #11-27odd, Weeks Money Saved ($) 28. y = 5x y = 8x Answer: 3 weeks y = 15x y = -20x Answer: 4 minutes Height (m) Minutes

Substitution: a method to solve a system of equations. A. Use substitution to solve the system of equations. x = 4y 4x – y = 75 Answer: (20, 5) 5-2 Substitution Step 1: Since x = 4y, substitute 4y for x in the 2 nd equation. 4(4y) – y = 75 16y – y=75 15y=75 y = 5 Step 2: Use x = 4y to find the value of x. x = 4y x = 4(5) x = 20

Lesson 2 Ex1 B. Use substitution to solve the system of equations. 4x + y = 12 –2x – 3y = 14 Answer: (5, -8) First, solve the first equation for y since the coefficient of y is 1. 4x + y = 12 y = -4x + 12 Then find the value of x by substituting -4x + 12 for y in the second equation. –2x – 3y=14 –2x – 3(-4x+12)=14 –2x +12x – 36=14 10x – 36=14 10x=50 x = 5 Lastly, substitute 5 for x in either equation to find the value of y. y = -4x + 12 y = -4(5) + 12 y = y = –8

Lesson 2 Ex2 Use substitution to solve the system of equations. A. 2a + 2b = 8 a + b = –2 Answer: No solution B. 6x – 2y = -4 y = 3x + 2 Answer: Infinitely many a = -b – 2 2(-b – 2) + 2b = 8 -2b – 4 + 2b = 8 -4 = 8 6x – 2(3x + 2) = -4 6x – 6x – 4 = = -4

1.A 2.B 3.C 4.D Lesson 2 CYP3 Answer: 2 mL of 10% HCl solution, 8 mL of 40% HCl solution CHEMISTRY Michael needs 10 milliliters of 34% HCl (hydrochloric acid) solution for a chemistry experiment. There is a bottle of 10% HCl solution and a bottle of 40% HCl solution in the lab. How much of each solution should he use to obtain the required amount of 34% HCl solution? (Think back to chapter 2… this time we will use 2 equations instead) Given information 10 mL 34% HCL x mL 10% HCL y mL40% HCL System of Equations x + y = x y = 0.34(10) Solve y = 10 – x 0.10x (10 – x) = x + 4 – 0.4x = x = -6 x = 2 y = 10 – x y = 10 – 2 y = 8

1.A 2.B 3.C 4.D Amy and Rachel are both saving money for a summer vacation. Amy has already saved $100 and plans to save $25 per week until the trip. Rachel has $75 and plans to save $30 per week. In how many weeks will they have the same amount of money? Graph the system of equations to find the answer. (Hint: Go by 25 for the y scale). Use may use Graphing calculator: 1. Enter equations in y= 2. 2 nd [Calc] 5 Enter Enter Enter Answer: 5 weeks 12-9 Honors Algebra Warm-up