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bazaltina [42]
3 years ago
10

solve the system of equations by finding the reduced row-echelon form of the augmented matrix for the system of equations. x-2y+

3z=-2. 6x+2y+2z=-48. x+4y+3z=-38​
Mathematics
1 answer:
Alekssandra [29.7K]3 years ago
7 0

Answer:

x = -5, y = -6, z = -3

Step-by-step explanation:

Given the system of three equations:

\left\{\begin{array}{l}x-2y+3z=-2\\6x+2y+2z=-48\\x+4y+3z=-38\end{array}\right.

Write the augmented matrix for the system of equations

\left(\begin{array}{ccccc}1&-2&3&|&-2\\6&2&2&|&-48\\1&4&3&|&-38\end{array}\right)

Find the reduced row-echelon form of the augmented matrix for the system of equations:

\left(\begin{array}{ccccc}1&-2&3&|&-2\\6&2&2&|&-48\\1&4&3&|&-38\end{array}\right)\sim \left(\begin{array}{ccccc}1&-2&3&|&-2\\0&-14&16&|&36\\0&-6&0&|&36\end{array}\right)\sim \left(\begin{array}{ccccc}1&3&-2&|&-2\\0&16&-14&|&36\\0&0&-6&|&36\end{array}\right)

Thus, the system of three equations is

\left\{\begin{array}{r}x+3z-2y=-2\\16z-14y=36\\-6y=36\end{array}\right.

From the last equation:

y=-6

Substitute it into the second equation:

16z-14\cdot (-6)=36\\ \\16z=36-84\\ \\16z=-48\\ \\z=-3

Substitute y = -6 and z = -3 into the first equation:

x+3\cdot (-3)-2\cdot (-6)=-2\\ \\x=-2+9-12\\ \\x=-5

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2 years ago
Suppose that a family wants to increase the size of the garden which is currently 16 feet long and 8 feet wide without changing
Cloud [144]

Answer:

See below

Step-by-step explanation:

<u>Sides of the garden</u>

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<u>New dimensions of the garden</u>

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<u>1. The area of the new garden</u>

  • (16 + 2x)(8 + x) =
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<u>2. The difference in area </u>

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<u>3. x= 2 effect on the area</u>

  • 2*2^2 + 32*2 =
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<u>4. Area difference = 160</u>

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<u>5. Area difference = 4 times</u>

  • 2x^2 + 32x = 128*3
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3 0
3 years ago
Interpret (1,15)<br><br> interpret (4,60)
statuscvo [17]

Interpreting (1,15) with (4,60), found that (4,60) is 4 times of the coordinate (1,15).

<h3>What are coordinates?</h3>

A pair of numbers that describe the position of a point on a coordinate plane by using the horizontal and vertical distances from the two reference axes.

For interpreting we have to find the relation between (1,15) and (4,60)

We have, (1,15)

For x- coordinate 1, y- coordinate will be 15

Now,

let us take x- coordinate=2 then y- coordinate =30

again, if x-coordinate = 3 then y-coordinate  = 45

lastly, if the x-coordinate =4 then y-coordinate = 60

That means (4,60) is the 4 times of the coordinate (1,15) i.e., the x-coordinate is 4 times as well as the y- coordinate is 4 times.

Learn more about coordinates here:

brainly.com/question/23450276

#SPJ1

4 0
2 years ago
A carpenter needs 36 screws that are 1.5 inches long, 24 screws that are 2 inches long, and 12 screws that are 2.5 inches long.
Neporo4naja [7]
48/132
You’re welcome
4 0
3 years ago
Find the greatest common factor!<br> Please help with these 2 questions
Aleksandr-060686 [28]

Hello!

The greatest common factor (GCF) is self explanatory. We find the factors of each number, and find the largest ones that are in common

12: 1,12,2,6,3,4

33:1,33,3,11,

As you can see, the greatest number these two have in common is 3.

Now for the next set.

45: 1,45,3,15,5,9

70:1,70,2,35,5,14,7,10

As you can see, our GCF is 5.

Therefore, our answers are below.

9) 3

10) 5

I hope this helps!

5 0
3 years ago
Read 2 more answers
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