{ { { { WARM-UP Date: 3/10/09 Solve the system. 12x + 4y = -8 Solve by graphing. 2. Solve the system. { 1. 12x + 4y = -8 y = x + 2 { 3x + 4y = 2 5x + 9y = 1 3. Solve the system. 4. Solve the system. { -3x = -2y – 37 x = 2y + 19 { 4x – 2y = -10 y = 2x + 5

{ 15x + 20y = 10 1. Solve the system. + -15x – 27y = -3 -7y = 7 -7 -7 = 10 1. Solve the system. + -15x – 27y = -3 -7y = 7 -7 -7 { 5( ) y = -1 3x + 4y = 2 5x + 9y = 1 -3( ) 3x + 4y = 2 3x + 4 (-1) = 2 3x – 4 = 2 +4 +4 3x = 6 3 3 x = 2 Solution (1, -1)

2. Find the solution to the systems by graphing. 12x + 4y = -8 -12x -12x y = x + 2 2. Find the solution to the systems by graphing. 4y = -8 – 12x 4 4 y = -2 – 3x { 12x + 4y = -8 y = x + 2 Solution (-1, 2)

{ Substitute the x: -3(2y + 19) = -2y – 37 3. Use substitution to solve systems. -6y – 57 = -2y – 37 +2y +2y -4y – 57 = -37 { -3x = -2y – 37 x = 2y + 19 +57 +57 -4y = 20 -4 -4 y = -5 x = 2y + 19 Substitute the y: x = 2(-5) + 19 x = 9 x, y Solution: (9, -5)

{ 4x – 2(2x + 5) = -10 Solve by substitution. 4x – 4x – 10 = -10 4. Solve by substitution. 4x – 4x – 10 = -10 { 4x – 2y = -10 y = 2x + 5 0x – 10 = -10 -10 = -10 Is this a true? YES Infinite Solutions

Solving Word Problems with Systems Name: Pd Algebra 3/10/09

Word Problem Steps Figure out what the question is. Determine what the variables need to be. Find key numbers. Create Equations. Solve.

p: Ex1: Paula went to get school supplies. If she buys 8 pencils and 5 notebooks it will cost $8.30. If she buys 12 pencils and 3 notebooks it will cost $5.70. Write a system describing the cost of a pencil, p, and notebook, n. cost of pencils n: cost of notebooks { 8p + 5n = 8.30 12p + 3n = 5.70

f: Ex2: Rob bought 15 concert tickets worth $322.50. Floor tickets cost $25 each while the balcony tickets cost $17.50 each. Write a system for the number of balcony seats, b and floor seats, f, purchased. # of floor seats b: # of balcony seats { 25f + 17.50b = 322.50 f + b = 15

d: Ex3: Micah has a total of $3.35 in dimes and quarters. If he has 14 coins, write an equation for finding the number of dimes, d, and quarters, q. # of dime q: # of quarter { 0.10d + 0.25q = 3.35 d + q = 14

c: Ex4: Jamie has 78 rock and country CDs in his collection. The number of country CDs he has is 7 less than 3 times the number of rock CDs he has. Write a system for finding the number of rock, r, and c, country CDs he has. # of country CDs r: # of rock CDs { c = 3r – 7 r + c = 78

Ex5: Fred went to the fruit stand to purchase oranges and bananas Ex5: Fred went to the fruit stand to purchase oranges and bananas. He can purchase 5 oranges and 6 bananas for $2.05 or he can purchase 7 oranges and 8 bananas for $2.79. What is the cost of each orange and banana? R: Cost of a orange B: Cost of a banana { 7( ) 5R + 6B = 2.05 -5( ) 7R + 8B = 2.79 35R + 42B = 14.35 + -35R – 40B = -13.95 2B = 0.40 2 2 B = 0.2 Bananas $0.20.

Ex5: Fred went to the fruit stand to purchase oranges and bananas Ex5: Fred went to the fruit stand to purchase oranges and bananas. He can purchase 5 oranges and 6 bananas for $2.05 or he can purchase 7 oranges and 8 bananas for $2.79. What is the cost of each orange and banana? B = 0.2 5R + 6B = 2.05 5R + 6(0.2) = 2.05 5R +1.2 = 2.05 -1.2 -1.2 5R = 0.85 5 5 R = 0.17 Oranges $0.17

Ex6: At a small town baseball game there were 78 people Ex6: At a small town baseball game there were 78 people. Children tickets were $2 and adult tickets were $7. If $421 was made at the game, how many adults went? a: Number of adults b: Number of children { 7a + 2c = 421 -2( ) a + c = 78 7a + 2c = 421 -2a – 2c = -156 + 5a = 265 5 5 a = 53 53 adults

{ R: # hours Rachel worked Ex7: Rachel and Bob work as part-time employees for a lawyer. Last weeks Rachel worked 4 hours less than Bob worked. Together they worked 38 hours total. How many hours did Bob and Rachel work? B: # hours Bob worked { R = B – 4 R + B = 38 B – 4 + B = 38 2B – 4 = 38 + 4 +4 2B = 44 2 2 B = 22 Bob worked 22 hours.

Ex7: Rachel and Bob work as part-time employees for a lawyer Ex7: Rachel and Bob work as part-time employees for a lawyer. Last weeks Rachel worked 4 hours less than Bob worked. Together they worked 38 hours total. How many hours did Bob and Rachel work? B = 22 R = B – 4 R = 22 – 4 R = 18 Rachel worked 18 hours.

{ L: length of a rectangle Ex8: The length of a rectangle is 4 meters less than three times its width. If the perimeter of the rectangle is 48 meters, then what is the value of the length (in meters)? W: width of a rectangle { L = 3w – 4 2W + 2L = 48 2w + 2(3w – 4) = 48 2w + 6w – 8 = 48 8w – 8 = 48 + 8 +8 8w = 56 8 8 w = 7 Width 7 meters.

Ex8: The length of a rectangle is 4 meters less than three times its width. If the perimeter of the rectangle is 48 meters, then what is the value of the length (in meters)? w = 7 L = 3(7) – 4 L = 21 – 4 L = 17 Length is 17 m.

Complete your practice packets to be turned in at the end of class If you finish early please begin your exit ticket and begin your homework.