Name: Quadratic Equation Word Problems
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Chapters

Exercise 1
Exercise 2
Exercise 3
Exercise 4
Exercise 5
Exercise 6
Exercise 7
Exercise 8
Solution of exercise 1
Solution of exercise 2
Solution of exercise 3
Solution of exercise 4
Solution of exercise 5
Solution of exercise 6
Solution of exercise 7
Solution of exercise 8

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Exercise 1

Solve:

$\text{[math]}$

Exercise 2

Solve:

$\text{[math]}$

Exercise 3

Solve:

$\text{[math]}$

Exercise 4

Consider the following system for different values of a and b:

$\text{[math]}$

Exercise 5

Solve:

$\text{[math]}$

Exercise 6

Consider the following system for different values of a and b:

$\text{[math]}$

Exercise 7

Determine for what values of k, the following system has infinite solutions:

$\text{[math]}$

Exercise 8

Solve:

$\text{[math]}$

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Solution of exercise 1

Solve:

$\text{[math]}$ $\text{[math]}$ $\text{[math]}$ $\text{[math]}$ $\text{[math]}$ $\text{[math]}$ $\text{[math]}$ $\text{[math]}$ $\text{[math]}$ $\text{[math]}$ $\text{[math]}$ $\text{[math]}$

If a= $\text{[math]}$ , r(A) = r(A')=2, n=3

$\text{[math]}$ $\text{[math]}$

If $\text{[math]}$ , this means that the system is a consistent independent system!

$\text{[math]}$ $\text{[math]}$ $\text{[math]}$ $\text{[math]}$

Solution of exercise 2

Solve:

$\text{[math]}$

$\text{[math]}$ $\text{[math]}$ $\text{[math]}$

Supposing $\text{[math]}$ :

$\text{[math]}$ $\text{[math]}$

$\text{[math]}$ , this means that the system is a consistent dependent system!

$\text{[math]}$ , supposing $\text{[math]}$

$\text{[math]}$ $\text{[math]}$

In case, $\text{[math]}$ , this means that the system is a consistent independent system!

$\text{[math]}$ $\text{[math]}$ $\text{[math]}$ $\text{[math]}$

Solution of exercise 3

Solve:

$\text{[math]}$ $\text{[math]}$ $\text{[math]}$ $\text{[math]}$

If $\text{[math]}$

$\text{[math]}$ $\text{[math]}$

$\text{[math]}$

$\text{[math]}$ , this means that the system is an inconsistent system!

If $\text{[math]}$ this means that the system is a consistent independent system!

$\text{[math]}$

Applying row operation $\text{[math]}$ :

$\text{[math]}$ $\text{[math]}$

Solution of exercise 4

Consider the following system for different values of a and b:

$\text{[math]}$ $\text{[math]}$ $\text{[math]}$ $\text{[math]}$

$\text{[math]}$ , this means that the system is a consistent independent system!

If $\text{[math]}$ :

$\text{[math]}$ $\text{[math]}$ $\text{[math]}$

$\text{[math]}$ , this means that the system is an Inconsistent system!

Otherwise $\text{[math]}$ , this means that the system is a consistent dependent system!

If $\text{[math]}$ :

$\text{[math]}$ $\text{[math]}$ $\text{[math]}$ $\text{[math]}$

$\text{[math]}$ , this means that the system is an Inconsistent system!

Solution of exercise 5

Solve:

$\text{[math]}$ $\text{[math]}$

We will be using row operations:

$\text{[math]}$ $\text{[math]}$ $\text{[math]}$ $\text{[math]}$ $\text{[math]}$ $\text{[math]}$ $\text{[math]}$

Finding the value of a from the 3rd row:

$\text{[math]}$ $\text{[math]}$

In the third row, $\text{[math]}$ means that the system is a consistent dependent system.

$\text{[math]}$ $\text{[math]}$

$\text{[math]}$ which means inconsistent system.

Solution of exercise 6

Consider the following system for different values of a and b:

$\text{[math]}$ $\text{[math]}$

Applying these row operations:

$\text{[math]}$ $\text{[math]}$ $\text{[math]}$ $\text{[math]}$ $\text{[math]}$

$\text{[math]}$ , hence it is a consistent indendent system

$\text{[math]}$

$\text{[math]}$ which indicates that the system is an inconsistent system

$\text{[math]}$ which indicates that the system is a consistent dependent system

$\text{[math]}$ $\text{[math]}$

Solution of exercise 7

Determine for what values of k, the following system has infinite solutions:

$\text{[math]}$ $\text{[math]}$

Applying row operations:

$\text{[math]}$

$\text{[math]}$ * 2 was taken as common and divided by 0

$\text{[math]}$ $\text{[math]}$ $\text{[math]}$ $\text{[math]}$ $\text{[math]}$

Solution of exercise 8

Solve:

$\text{[math]}$ $\text{[math]}$

Applying these row operations:

$\text{[math]}$ $\text{[math]}$

$\text{[math]}$ , this means that the system is an inconsistent system (for any value of m)

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Linear System of Equations with Parameters Exercises

Exercise 1

Exercise 2

Exercise 3

Exercise 4

Exercise 5

Exercise 6

Exercise 7

Exercise 8

Solution of exercise 1

Solution of exercise 2

Solution of exercise 3

Solution of exercise 4

Solution of exercise 5

Solution of exercise 6

Solution of exercise 7

Solution of exercise 8

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Equivalent Equations

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Quadratic Equation Word Problems

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