Precalculus with Limits
Precalculus with Limits
3rd Edition
ISBN: 9781133947202
Author: Ron Larson
Publisher: Cengage Learning
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Chapter 7.1, Problem 14E
To determine

The solution of the system of equations by substitution method. The solution is verified by graphically.

Expert Solution & Answer
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Answer to Problem 14E

  {(0,1),(3,1),(1,−1)}

Explanation of Solution

Given information:

The system of the equation are:

  {y=x3−3x2+1y=x2−3x+1

Calculation:

The given equations are {y=x3−3x2+1y=x2−3x+1 .

To find the system of the equation firstly will isolate one of the variable in terms of the other and substitute it into the other equation, then solve for the remaining variable are as shown below:

From the system of the equation, notice y is already solved. Now substitute the first or second equation into the other one.

  x2−3x+1=x3−3x2+1

Add the above equations:

  x3−4x2+3x=0

By factorisation of the equation:

  x(x2−4x+3)=0x(x−3)(x−1)=0

There are three solutions x=0,3,1 .By substituting these values in the given equation get y=1,1, and −1 .

The solutions are {(0,1),(3,1),(1,−1)} .

Now, verify the given equation by graphically are as shown below:

  Precalculus with Limits, Chapter 7.1, Problem 14E Thus,the solutions are {(0,1),(3,1),(1,−1)} .

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Chapter 7.1, Problem 13E
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Chapter 7.1, Problem 15E

Chapter 7 Solutions

Precalculus with Limits

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Ch. 7.1 - Prob. 11ECh. 7.1 - Prob. 12ECh. 7.1 - Prob. 13ECh. 7.1 - Prob. 14ECh. 7.1 - Prob. 15ECh. 7.1 - Prob. 16ECh. 7.1 - Prob. 17ECh. 7.1 - Prob. 18ECh. 7.1 - Prob. 19ECh. 7.1 - Prob. 20ECh. 7.1 - Prob. 21ECh. 7.1 - Prob. 22ECh. 7.1 - Prob. 23ECh. 7.1 - Prob. 24ECh. 7.1 - Prob. 25ECh. 7.1 - Prob. 26ECh. 7.1 - Prob. 27ECh. 7.1 - Prob. 28ECh. 7.1 - Prob. 29ECh. 7.1 - Prob. 30ECh. 7.1 - Prob. 31ECh. 7.1 - Prob. 32ECh. 7.1 - Prob. 33ECh. 7.1 - Prob. 34ECh. 7.1 - Prob. 35ECh. 7.1 - Prob. 36ECh. 7.1 - Prob. 37ECh. 7.1 - Prob. 38ECh. 7.1 - Prob. 39ECh. 7.1 - Prob. 40ECh. 7.1 - Prob. 41ECh. 7.1 - Prob. 42ECh. 7.1 - Prob. 43ECh. 7.1 - Prob. 44ECh. 7.1 - Prob. 45ECh. 7.1 - Prob. 46ECh. 7.1 - Prob. 47ECh. 7.1 - Prob. 48ECh. 7.1 - Prob. 49ECh. 7.1 - Prob. 50ECh. 7.1 - Prob. 51ECh. 7.1 - Prob. 52ECh. 7.1 - Prob. 53ECh. 7.1 - Prob. 54ECh. 7.1 - Prob. 55ECh. 7.1 - Prob. 56ECh. 7.1 - Prob. 57ECh. 7.1 - Prob. 58ECh. 7.1 - Prob. 59ECh. 7.1 - Prob. 60ECh. 7.1 - Prob. 61ECh. 7.1 - Prob. 62ECh. 7.1 - Prob. 63ECh. 7.1 - 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