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andrey2020 [161]
3 years ago
6

Solve the system using either Gaussian elimination with back-substitution or Gauss-Jordan elimination. (If there is no solution,

enter NO SOLUTION. If the system has an infinite number of solutions, set y = t and solve for x in terms of t.) −3x + 5y = −34 3x + 4y = −11 4x − 8y = 52
Mathematics
1 answer:
Katyanochek1 [597]3 years ago
4 0

Answer:

The solution of the system of equations is x=3\\y=-5.

Step-by-step explanation:

Gauss–Jordan elimination is a procedure for converting a matrix to reduced row echelon form using elementary row operations.

It relies upon three elementary row operations one can use on a matrix:

  1. Swap the positions of two of the rows
  2. Multiply one of the rows by a nonzero scalar.
  3. Add or subtract the scalar multiple of one row to another row.

To find the solution of the system

-3x + 5y = -34 \\3x + 4y = -11 \\4x -8y = 52

using Gauss-Jordan elimination you must:

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

In an augmented matrix, each row represents one equation in the system and each column represents a variable or the constant terms.

This is the augmented matrix that represents the system.

\left[ \begin{array}{ccc} -3 & 5 & -34 \\\\ 3 & 4 & -11 \\\\ 4 & -8 & 52 \end{array} \right]

Using elementary matrix operations, we get that

Row Operation 1: Add row 1 to row 2 \left(R_2=R_2+R_1\right)

Row Operation 2: Divide row 1 by −3 \left(R_1=\frac{R_1}{-3}\right)

Row Operation 3: Subtract row 1 multiplied by 4 from row 3 \left(R_3=R_3-\left(4\right)R_1\right)

Row Operation 4: Divide row 2 by 9 \left(R_2=\frac{R_2}{9}\right)

Row Operation 5: Add row 2 multiplied by 5/3 to row 1 \left(R_1=R_1+\left(\frac{5}{3}\right)R_2\right)

Row Operation 6: Add row 2 multiplied by 4/3 to row 3 \left(R_3=R_3+\left(\frac{4}{3}\right)R_2\right)

This is the reduced row echelon form matrix

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

Step 2: Interpret the reduced row echelon form

The reduced row echelon form of the augmented matrix corresponds to the system

x=3\\y=-5

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Answer:

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Step-by-step explanation:

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Percentage of students scored below 300 is given by,

P(Z\leq \frac{x-\mu}{\sigma})\times 100

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90th percentile is such that,

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~~~ 30 POINTS ~~~
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<span>1)   3x-2=x+10


</span><span>Now, lets solve this step-by-step.
</span><span>
3x - 2 = x + 10
-x             -x
</span><span>
</span><span>3x - x = 2x                                2x - 2 = 10
</span><span>
</span><span>2x - 2 = 10
</span>2x - 2+2 = 10+2          The inverse operation helps isolate the variable. 
<span>
2x = 12

2x/2 = 12/2

x = 12/2
x = 6</span><span>

Answer: x = 6

2) x + 4 = 19 - 2x </span>

We can solve this much faster

x + 4 = 19 - 2x
                  +2x

x+2x = 3x

3x + 4 = 19
      -4     -4

19-4 = 15

3x= 15
3x/3 = 15/3
x= 5

Answer: x = 5

3) 
<span>8x - 20 = x + 15

Much faster now!!

8x - 20 = x + 15
               -x
8x-x = 7x

7x - 20 = 15
      +20   +20
15+20 = 35

7x = 35
7x/7 = 35/7
x = 35/7
x = 5

Answer: x= 5</span>
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