Get variables on the same side & line up x, y, and z

-x + 2y – z = 5 x – 3y – 2z = -7 -y – 3z = -2 2x + 4y + 3z =6 -2x + 6y + 4z = 14 10y + 7z = 20 (-1)( ) (-1) (-2)( ) (-2)

-10y – 30z = y + 7z = z = 0 z = 0 (-1, 2, 0) 10y + 7(0) = 20 10y = 20 y = 2 x – 2(0) = 3(2) – 7 x – 0 = 6 – 7 x = -1 (10)( ) (10)

Thurs 10/22 Lesson 3 – 5 Learning Objective: To solve word problems with systems Hw: Lesson 3 – 5 Word Problems WS

Algebra II

 To solve word problems using systems of equations

1. Find the value of two numbers if their sum is 19 and their difference is 3. x + y = 19 x – y = 3 2x = 22 x = y = 19 y = 8 {8, 11}

2. On the first day of choir ticket sales, 12 adults and 1 student ticket sold for a total of $171. Choir took in $138 on the second day be selling 6 adult tickets and 4 student tickets. Find the price of an adult and a student ticket. 12x + y = 171 6x + 4y = 138 (-4) -48x - 4y =-684 6x + 4y = x = -546 x = 13 12(13) + y = y = 171 y = 15 $13 for adult tix $15 for student tix

3. Jacob sold 14 banana pies and 13 strawberry pies for a total of $241. Kim sold 2 banana pies and 6 strawberry pies for a total of $80. What is the cost of each pie? 14x + 13y = 241 2x + 6y = 80 (-7) 14x + 13y = x -42y = y = -319 y = 11 2x + 6(11) = 80 2x + 66 = 80 2x = 14 x = 7 $7 for banana pie $11 for strawberry

4. The sum of three numbers is 6. The third number is the sum of the first and second number. The first number is one more than the third number. Find the numbers. x = 1 st #y = 2 nd #z = 3 rd # x + y + z = 6 z = x + y x = z + 1 x + y + z = 6 x + y – z = 0 x - z = 1

4. x – 3 = 1 x = 4 x + y + z = 6 x + y – z = 0 x - z = 1 (-1) -x - y - z = -6 x + y – z = 0 -2z = -6 z = y + 3 = y = 6 y = -1 {4, -1, 3}

5. Anna is training for a triathlon. In her training routine each week, she runs 7 times as far as she swims and she bikes 3 times as far as she runs. One week, she trained a total of 232 miles. How far did she run that week? x = swimy = runz = bike x + y + z = 232 y = 7x z = 3y x + y + z = x + y = 0 -3y + z = 0

5. -7x + y = 0 x + 4y = 232 x + y + z = x + y = 0 -3y + z = 0 (-1) x + y + z = 232 3y – z = 0 x + 4y = 232 (-4) 28x -4 y = 0 x + 4y = x = 232 x = 8

5. y=7(8) y = 56 z = 3(56) z = 168 Swim 8 miles Run 56 miles Bike 168 miles

6. Sports Chalet sold 10 gloves, 3 bats, and 2 bases for $99 on Monday. On Tuesday, it sold 4 gloves, 8 bats, and 2 bases for $78. On Wednesday, it sold 2 gloves, 3 bats, and 1 base for $ What are the prices of each item? x = glovey = batz = base 10x + 3y + 2z = 99 4x + 8y + 2z = 78 2x + 3y + z = 33.60

6. 10x + 3y + 2z = 99 -4x – 6y – 2z = x – 3y = x + 3y + 2z = 99 4x + 8y + 2z = 78 2x + 3y + z = (-1) 10x + 3y + 2z = 99 -4x – 8y – 2z = -78 6x – 5y = 21 (-2)

6. 6x – 5y = 21 6x – 3y = 31.8 (-1) Glove $8 Bat $5.40 Base $ x + 5y = -21 6x – 3y = y = 10.8 y = 5.4 6x – 3(5.4) = x – 16.2 = x = 48 x = 8 4(8) + 8(5.4) + 2z = z = z = 78z = 1.4

7. The sum of three numbers is -4, The second number decreased by the third number is equal to the first. The sum of the first and second number is -6. What are the numbers? x = 1 st #y = 2 nd #z = 3 rd # x + y + z = -4 y – z = x x + y = -6 x + y + z = -4 -x + y – z = 0 x + y = -6

7. x + (-2) = -6 x = -4 x + y + z = -4 -x + y – z = 0 x + y = -6 x + y + z = -4 -x + y – z = 0 2y = -4 y = (-2) + z = z = -4 z = 2 {-4, -2, 2}

8. The difference of two number is 2. Their sum if 20. What are the numbers? x + y = 20 x – y = 2 2x = 22 x = y = 20 y = 9 {9, 11}

 LAHS scored 37 points in a football game. Six points are award for each touchdown. After each touchdown, the team can earn one point for the extra kick, or two points for a 2-point conversion. The team scored one fewer 2-point conversions than extra kicks. The team scored 10 times during the game. How many touchdowns were made?