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Triss [41]
3 years ago
10

3x + 2y + z = 8 2x - 3y + 2z = -16 x + 4y - z = 20

Mathematics
1 answer:
padilas [110]3 years ago
4 0
I'll do a similar problem, and I challenge you to do this on your own using similar methods!

x+5y+2z=23
8x+4y+3z=12
9x-3y-7z=-10

Multiplying the first equation by -8 and adding it to the second one (to get rid of the x) and also multiplying the first equation by -9 and adding the third one to get rid of the x there too, we end up with

-36y-13z=-92
and
-48y-25z=-217

Multiplying both equations by -1, we get
36y+13z=-92
48y+25z=217

Multiplying the (new) first equation by -4/3 and adding it to the second (to get rid of the y), we get
(7+2/3)z=94+1/3

Dividing both sides by (7+2/3) to separate the z, we get
z=\frac{282/3}{23/3} = \frac{282}{23}

Plugging that into 
48y+25z=217, we can subtract 25z from both sides and divide by 48 to get 
y= \frac{217-25z}{48} =\frac{217-25*282/23}{48}

Lastly, we plug this into x+5y+2z=23 to get
x=23-5y-2z by subtracting 5y+2z from both sides to get 
x=23- \frac{217-25*282/23}{48}*5-2*282/23 

Good luck, and feel free to ask with any questions!
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What is the determinant of A = [ -2 2 -5 4 -1 -2 1 3 -5]
stepan [7]

Answer:

-51

Step-by-step explanation:

\begin{vmatrix}-2&2&-5\\4&-1&-2\\1&3&-5\end{vmatrix}=\\=\mathsf{-10-4-60-5+40-12}=\\=\mathsf{-91+40}=\\=\mathsf{-51}

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3 years ago
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Tim will borrow $6200 at 12.5% APR. He will pay it back over 2 years. What will be his Monthly payment be?
AlekseyPX
<span>The correct answer is D) $293.32.

Explanation:
We use the formula P=A/D, where P is the payment amount, A is the amount borrowed, and D is the discount factor.

The discount factor is given by the formula D={[(1+r)^n]-1}/[i(1+i)^n], where i is the monthly interest rate as a decimal number and n is the number of months taken for repayment.

For this problem, we have 12.5%; 12.5%=12.5/100=0.125.
This makes the monthly interest rate, i, 0.125/12=0.01042.
 
The number of months for repayment, n, will be 2*12=24.

Using these we have D={[1+0.01042)^24]-1}/[0.01042(1+0.01042)^24], which gives us D=21.1375.

We plug this in for D in our payment formula.

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3 0
3 years ago
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3. Solve using substitution.<br> x - y = 4<br> 3x - 2y = -5
Vedmedyk [2.9K]

<u>Given</u>:

The system of linear equations are x-y=4 and 3x-2y=-5

We need to determine the solution to the system of equations using substitution method.

<u>Solution</u>:

The solution can be determined using the substitution method.

Let us substitute x=4+y in the equation 3x-2y=-5

Thus, we have;

3(4+y)-2y=-5

12+3y-2y=-5

          12+y=-5

                  y=-17

Thus, the value of y is -17.

Substituting y=-17 in the equation x-y=4, we get;

x+17=4

       x=-13

Thus, the value of x is -13.

Hence, the solution to the system of equations is (-13,-17)

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