Download presentation

Presentation is loading. Please wait.

1
Sample Questions 91587

2
**Example 1 Billy’s Restaurant ordered 200 flowers for Mother’s Day. **

They ordered carnations at $1.50 each, roses at $5.75 each, and daisies at $2.60 each. They ordered mostly carnations, and 20 fewer roses than daisies. The total order came to $ How many of each type of flower was ordered?

3
Decide your variables Billy’s Restaurant ordered 200 flowers for Mother’s Day. They ordered carnations at $1.50 each, roses at $5.75 each, and daisies at $2.60 each. They ordered mostly carnations, and 20 fewer roses than daisies. The total order came to $ How many of each type of flower was ordered?

4
Write the equations Billy’s Restaurant ordered 200 flowers for Mother’s Day. c + r + d = 200 They ordered carnations at $1.50 each, roses at $5.75 each, and daisies at $2.60 each. 1.5c r + 2.6d = They ordered mostly carnations, and 20 fewer roses than daisies. d – r = 20 The total order came to $ How many of each type of flower was ordered?

5
Order the equations Billy’s Restaurant ordered 200 flowers for Mother’s Day. c + r + d = 200 They ordered carnations at $1.50 each, roses at $5.75 each, and daisies at $2.60 each. 1.5c r + 2.6d = They ordered mostly carnations, and 20 fewer roses than daisies. d – r = 20 The total order came to $ How many of each type of flower was ordered?

6
**Solve using your calculator and answer in context**

There were 80 carnations, 50 roses and 70 daisies ordered.

7
Example 2 If possible, solve the following system of equations and explain the geometrical significance of your answer.

8
**Calculator will not give you an answer.**

If possible, solve the following system of equations and explain the geometrical significance of your answer.

9
**Objective - To solve systems of linear equations in three variables.**

10
**There is no solution. The three planes form a tent**

shape and the lines of intersection of pairs of planes are parallel to one another Inconsistent, No Solution

11
Example 2 Solve the system of equations using Gauss-Jordan Method

12
Example Solve the system of equations using Gauss-Jordan Method

13
Example Solve the system of equations using Gauss-Jordan Method

14
Example Solve the system of equations using Gauss-Jordan Method

15
**Example Solve the system of equations using Gauss-Jordan Method**

No solution

16
Example 3 Consider the following system of two linear equations, where c is a constant: Give a value of the constant c for which the system is inconsistent. If c is chosen so that the system is consistent, explain in geometrical terms why there is a unique solution.

17
**Give a value of the constant c for which the system is inconsistent.**

The lines must be parallel but not a multiple of each other c = 10

18
If c is chosen so that the system is consistent, explain in geometrical terms why there is a unique solution. It means that the 2 lines must have different gradients so they intersect to give a unique solution.

19
Example 4 The Health Club serves a special meal consisting of three kinds of food, A, B and C. Each unit of food A has 20 g of carbohydrate, 2 g of fat and 4 g of protein. Each unit of food B has 5 g of carbohydrate, 1 g of fat and 2 g of protein. Each unit of food C has 80 g of carbohydrate, 3 g of fat and 8 g of protein. The dietician designs the special meal so that it contains 140 g of carbohydrate, 11 g of fat and 24 g of protein. Let a, b and c be the number of units of food A, B and C f respectively) used in the special meal. Set up a system of 3 simultaneous equations relating a, b and c. Do not solve the equations.

20
**For this type of problem it is easier if you make a table**

The Health Club serves a special meal consisting of three kinds of food, A, B and C. Each unit of food A has 20 g of carbohydrate, 2 g of fat and 4 g of protein. Each unit of food B has 5 g of carbohydrate, 1 g of fat and 2 g of protein. Each unit of food C has 80 g of carbohydrate, 3 g of fat and 8 g of protein. The dietician designs the special meal so that it contains 140 g of carbohydrate, 11 g of fat and 24 g of protein. Let a, b and c be the number of units of food A, B and C f respectively) used in the special meal. Set up a system of 3 simultaneous equations relating a, b and c. Do not solve the equations.

21
Carbohydrate Fat Protein A B C

22
**Each unit of food A has 20 g of carbohydrate, 2 g of fat and 4 g of protein**

23
**Each unit of food B has 5 g of carbohydrate, 1 g of fat and 2 g of protein**

20 2 4 B 5 1 C

24
**Each unit of food C has 80 g of carbohydrate, 3 g of fat and 8 g of protein**

20 2 4 B 5 1 C 80 3 8

25
**Carbohydrate Fat Protein A 20 2 4 B 5 1 C 80 3 8 Total 140 11 24**

The dietician designs the special meal so that it contains 140 g of carbohydrate, 11 g of fat and 24 g of protein. Carbohydrate Fat Protein A 20 2 4 B 5 1 C 80 3 8 Total 140 11 24

26
Write the equations Carbohydrate Fat Protein A 20 2 4 B 5 1 C 80 3 8 Total 140 11 24

27
**Consider the following system of three equations in x, y and z.**

Example 5 Consider the following system of three equations in x, y and z. 4x + 3y + 2z = 11 3x + 2y + z = 8 7x + 5y + az = b Give values for a and b in the third equation which make this system: 1. inconsistent, 2. consistent, but with an infinite number of solutions.

28
**Add the first two equations and put it with the third equation**

Inconsistent Add the first two equations and put it with the third equation 4x + 3y + 2z = 11 3x + 2y + z = x + 5y + 3z = 19 7x + 5y + az = b a = 3, b ≠19

29
**Consistent with an infinite number of solutions**

Add the first two equations and put it with the third equation 4x + 3y + 2z = 11 3x + 2y + z = x + 5y + 3z = 19 7x + 5y + az = b a = 3, b = 19

30
Example 6 Consider the following system of three equations in x, y and z. 2x + 2y + 2z = 9 x + 3y + 4z = 5 Ax + 5y + 6z = B Give possible values of A and B in the third equation which make this system: 1. inconsistent. 2. consistent but with an infinite number of solutions.

31
**Example 6 2x + 2y + 2z = 9 x + 3y + 4z = 5 3x + 5y + 6z = 14**

Ax + 5y + 6z = B Ax + 5y + 6z = B 1. inconsistent. A = 3, B ≠ 14 2. consistent but with an infinite number of solutions. A = 3, B = 14

Similar presentations

Presentation is loading. Please wait....

OK

Solving Systems of Equations by Graphing

Solving Systems of Equations by Graphing

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on polynomials for class 9 free download Ppt on autonomous cars Ppt on environmental degradation vs industrial revolution Ppt on traction rolling stocks Ppt on orphans in india Free ppt on brain machine interface mit Ppt on acid-base indicators worksheets Field emission display ppt online Hrm ppt on recruitment and selection Ppt on water cycle for class 9