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Lubov Fominskaja [6]
3 years ago
8

The system of equations is given:

Mathematics
1 answer:
Nutka1998 [239]3 years ago
6 0

Answer:

x=-1/85; y=-283/85; z=2/17

Step-by-step explanation:

Using an algebraic method like elimination or substitution would take a lot of steps which could lead to mistake the calculations. In this case, I decided to use the Gaussian elimination. We can express the system in matrix form as follows:

\left[\begin{array}{ccc}2&-4&6\\9&-3&1\\5&0&9\end{array}\right] \left[\begin{array}{ccc}x\\y\\z\end{array}\right] =\left[\begin{array}{ccc}14\\10\\1\end{array}\right]

To begin the calculations, we write the system in augmented matrix form and use the Gaussian elimination:

\left[\begin{array}{ccccc}2&-4&6&|&14\\9&-3&1&|&10\\5&0&9&|&1\end{array}\right]

By applying the Gaussian elimination, the final matrix is the following:

\left[\begin{array}{ccccc}1&0&0&|&-1/85\\0&1&0&|&-283/85\\0&0&1&|&2/17\end{array}\right]

In order to verify the results, it´s enough to substitute the calculated values in the original equations to see if the equalities are correct. Here you can see the verification for all of the equations:

2(-1/85)-4(-283/85)+6(2/17)=14\\9(-1/85)-3(-283/85)+1(2/17)=10\\5(-1/85)+9(2/17)=1

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a. Demarcus' method is (d + d + 7) = 111/3

b. His brother's method is 3d + 3d + 3 × 7 = 111

c. The banker's method is 3(2d + 7) = 111

<h3>How to complete each person's method</h3>

Each pperson's method is the solution to a linear equation

<h3>What is a linear equation?</h3>

A linear equation is an equation in which the highest power of the unknown is 1.

<h3>a. How to complete Demarcus' method?</h3>

Since the equation is given by 3(d + d + 7) = 111 and demarcus was solving the equation and his first step was to divide both sides by 3, we have that

3(d + d + 7) = 111

(d + d + 7) = 111/3

d + d + 7 = 37

2d + 7 = 37

2d = 37 - 7

2d = 30

d = 30/2

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So, Demarcus' method is (d + d + 7) = 111/3

<h3>b. How to complete his brother's method?</h3>

Since the equation is given by 3(d + d + 7) = 111 and his brother started solving the equation by using the distributive property,we have that

3(d + d + 7) = 111

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d = 90/6

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So, his brother's method is 3d + 3d + 3 × 7 = 111

<h3>c. How to complete the banker's method?</h3>

Since the equation is given by 3(d + d + 7) = 111 and their banker started solving the equation by combining like terms, we have that

3(d + d + 7) = 111

3(2d + 7) = 111

6d + 21 = 111

6d = 111 - 21

6d = 90

d = 90/6

d = 15

So, the banker's method is 3(2d + 7) = 111

Learn more about linear equation here:

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1 year ago
Add<br>show all steps please
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