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Sample Questions. 91587. 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.  - PowerPoint PPT Presentation

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Sample Questions

Sample Questions91587Example 1Billys Restaurant ordered 200 flowers for Mothers 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 $589.50. How many of each type of flower was ordered?Decide your variablesBillys Restaurant ordered 200 flowers for Mothers 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 $589.50. How many of each type of flower was ordered?Write the equationsBillys Restaurant ordered 200 flowers for Mothers Day. c + r + d = 200They ordered carnations at $1.50 each, roses at $5.75 each, and daisies at $2.60 each.1.5c + 5.75r + 2.6d = 589.50 They ordered mostly carnations, and 20 fewer roses than daisies. d r = 20The total order came to $589.50. How many of each type of flower was ordered?Order the equationsBillys Restaurant ordered 200 flowers for Mothers Day. c + r + d = 200They ordered carnations at $1.50 each, roses at $5.75 each, and daisies at $2.60 each.1.5c + 5.75r + 2.6d = 589.50 They ordered mostly carnations, and 20 fewer roses than daisies. d r = 20The total order came to $589.50. How many of each type of flower was ordered?

Solve using your calculator and answer in contextThere were 80 carnations, 50 roses and 70 daisies ordered.

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

Calculator will not give you an answer.If possible, solve the following system of equations and explain the geometrical significance of your answer.

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

Solve.

9There is no solution. The three planes form a tent shape and the lines of intersection of pairs of planes are parallel to one anotherInconsistent, No Solution10Example 2Solve the system of equations using Gauss-Jordan Method

ExampleSolve the system of equations using Gauss-Jordan Method

ExampleSolve the system of equations using Gauss-Jordan Method

ExampleSolve the system of equations using Gauss-Jordan Method

ExampleSolve the system of equations using Gauss-Jordan Method

No solutionExample 3Consider 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.

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 = 10If 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.Example 4The 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. For this type of problem it is easier if you make a tableThe 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. CarbohydrateFatProteinABCEach unit of food A has 20 g of carbohydrate, 2 g of fat and 4 g of proteinCarbohydrateFatProteinA2024BCEach unit of food B has 5 g of carbohydrate, 1 g of fat and 2 g of proteinCarbohydrateFatProteinA2024B512CEach unit of food C has 80 g of carbohydrate, 3 g of fat and 8 g of proteinCarbohydrateFatProteinA2024B512C8038The dietician designs the special meal so that it contains 140 g of carbohydrate, 11 g of fat and 24 g of protein. CarbohydrateFatProteinA2024B512C8038Total1401124Write the equationsCarbohydrateFatProteinA2024B512C8038Total1401124

Example 5Consider the following system of three equations in x, y and z. 4x + 3y + 2z = 113x + 2y + z = 8 7x + 5y + az = bGive values for a and b in the third equation which make this system:1. inconsistent, 2.consistent, but with an infinite number of solutions.

InconsistentAdd the first two equations and put it with the third equation4x + 3y + 2z = 113x + 2y + z = 8 7x + 5y + 3z = 19 7x + 5y + az = b

a = 3, b 19

Consistent with an infinite number of solutionsAdd the first two equations and put it with the third equation4x + 3y + 2z = 113x + 2y + z = 8 7x + 5y + 3z = 19 7x + 5y + az = b

a = 3, b = 19

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 = BGive 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.

Example 6 2x + 2y + 2z = 9 x + 3y + 4z = 5 3x + 5y + 6z = 14Ax + 5y + 6z = B Ax + 5y + 6z = B

1. inconsistent. A = 3, B 142.consistent but with an infinite number of solutions. A = 3, B = 14