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3 years ago

Use elimination to solve each system of equations.

Mathematics

1 answer:

Allushta [10]3 years ago

7 0

Answer:

x=-3

Y=-5

Step-by-step explanation:

2x-y=-1 ×2

3x-2y=1. ×1

4x-2y= -2

3x-2y=1

eliminate y by subtracting

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Solve the given system of equations using either Gaussian or Gauss-Jordan elimination. (If there is no solution, enter NO SOLUTI

cricket20 [7]

Answer:

The system has infinitely many solutions

$\begin{array}{ccc}x_1&=&-x_3\\x_2&=&-x_3\\x_3&=&arbitrary\end{array}$

Step-by-step explanation:

Gauss–Jordan elimination is a method of solving a linear system of equations. This is done by transforming the system's augmented matrix into reduced row-echelon form by means of row operations.

An Augmented matrix, each row represents one equation in the system and each column represents a variable or the constant terms.

There are three elementary matrix row operations:

Switch any two rows
Multiply a row by a nonzero constant
Add one row to another

To solve the following system

$\begin{array}{ccccc}x_1&-3x_2&-2x_3&=&0\\-x_1&2x_2&x_3&=&0\\2x_1&+3x_2&+5x_3&=&0\end{array}$

Step 1: Transform the augmented matrix to the reduced row echelon form

$\left[ \begin{array}{cccc} 1 & -3 & -2 & 0 \\\\ -1 & 2 & 1 & 0 \\\\ 2 & 3 & 5 & 0 \end{array} \right]$

This matrix can be transformed by a sequence of elementary row operations

Row Operation 1: add 1 times the 1st row to the 2nd row

Row Operation 2: add -2 times the 1st row to the 3rd row

Row Operation 3: multiply the 2nd row by -1

Row Operation 4: add -9 times the 2nd row to the 3rd row

Row Operation 5: add 3 times the 2nd row to the 1st row

to the matrix

$\left[ \begin{array}{cccc} 1 & 0 & 1 & 0 \\\\ 0 & 1 & 1 & 0 \\\\ 0 & 0 & 0 & 0 \end{array} \right]$

The reduced row echelon form of the augmented matrix is

$\left[ \begin{array}{cccc} 1 & 0 & 1 & 0 \\\\ 0 & 1 & 1 & 0 \\\\ 0 & 0 & 0 & 0 \end{array} \right]$

which corresponds to the system

$\begin{array}{ccccc}x_1&&-x_3&=&0\\&x_2&+x_3&=&0\\&&0&=&0\end{array}$

The system has infinitely many solutions.

$\begin{array}{ccc}x_1&=&-x_3\\x_2&=&-x_3\\x_3&=&arbitrary\end{array}$

7 0

3 years ago

g Which of the following is not appropriate to use the t-confidence interval for . a. The sample is based on a simple random sam

KATRIN_1 [288]

Answer:

d. The population standard deviation is known.

Step-by-step explanation:

T-distribution or Z-distribution, which to use?

If we have the population standard deviation is known, we use the z-distribution.

Otherwise, if we only have the standard deviation for the sample, we use the t-distribution.

Which of the following is not appropriate to use the t-confidence interval for

When the population standard deviation is known, so letter d.

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3 years ago

Michael is placing cubic blocks into a box that measures 8 inches by 12 inches. each block is 1 cubic inch. he has packed the fi

Nikitich [7]

Answer:

960

Step-by-step explanation:

First of all we can find the volume of the whole box:

8×12×10=960

then find the area of the blocks:

1×1×1=1

Finally, we divide them to find how many fit in to the box:

960÷1=960

So 960 of the blocks will fit into the box.

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3 years ago

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The double dot plot shows the number of points scored by Sam and Daniel in 15 games. What is the difference between their median

just olya [345]

Answer:

4.9

Step-by-step explanation:

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2 years ago

Assume that you randomly select 6 cards from a deck of 52. what is the probability that all of the cards selected are hearts?

Ira Lisetskai [31]

There are 13 hearts in a 52 deck.

You can think about it like this:

P = (13/52)*(12/51)*(11/50)*(10/49)*(9/48)*(8/47) = 0.00008428903476

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3 years ago