Answer:
The solutions for the given system of equations are:
Step-by-step explanation:
Given the equation system:
We obtain the following matrix:
![\left[\begin{array}{cccc}3&1&4&-3\\-1&1&4&17\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D3%261%264%26-3%5C%5C-1%261%264%2617%5Cend%7Barray%7D%5Cright%5D)
<u>Step 1:</u> Multiply the fisrt row by 1/3.
![\left[\begin{array}{cccc}1&\frac{1}{3} &\frac{4}{3}&-1\\-1&1&4&17\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D1%26%5Cfrac%7B1%7D%7B3%7D%20%26%5Cfrac%7B4%7D%7B3%7D%26-1%5C%5C-1%261%264%2617%5Cend%7Barray%7D%5Cright%5D)
<u>Step 2:</u> Sum the first row and the second row.
![\left[\begin{array}{cccc}1&\frac{1}{3} &\frac{4}{3}&-1\\0&\frac{4}{3} &\frac{16}{3}&16\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D1%26%5Cfrac%7B1%7D%7B3%7D%20%26%5Cfrac%7B4%7D%7B3%7D%26-1%5C%5C0%26%5Cfrac%7B4%7D%7B3%7D%20%26%5Cfrac%7B16%7D%7B3%7D%2616%5Cend%7Barray%7D%5Cright%5D)
<u>Step 3:</u> Multiply the second row by 3/4.
![\left[\begin{array}{cccc}1&\frac{1}{3} &\frac{4}{3}&-1\\0&1 &4&12\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D1%26%5Cfrac%7B1%7D%7B3%7D%20%26%5Cfrac%7B4%7D%7B3%7D%26-1%5C%5C0%261%20%264%2612%5Cend%7Barray%7D%5Cright%5D)
<u>Step 4:</u> Multiply the second row by -1/3 and sum the the first row.
![\left[\begin{array}{cccc}1&0 &0&-5\\0&1 &4&12\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D1%260%20%260%26-5%5C%5C0%261%20%264%2612%5Cend%7Barray%7D%5Cright%5D)
The result of the reduced matrix is:
This is equal to:
These are the solutions for the system of equations in terms of z, where z can be any number.
Answer:
289.92
Step-by-step explanation:
Multiply the numbers together
Answer: h = 9
Step-by-step explanation: A system of linear equations is consistent when it has at least one solution.
The matrix given is:
![\left[\begin{array}{ccc}-15&21&h\\5&-7&-3\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-15%2621%26h%5C%5C5%26-7%26-3%5Cend%7Barray%7D%5Cright%5D)
Transform this matrix in a row-echelon form:
![\left[\begin{array}{ccc}-15&21&h\\0&0&-9+h\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-15%2621%26h%5C%5C0%260%26-9%2Bh%5Cend%7Barray%7D%5Cright%5D)
For this row-echelon form to have solutions:
-9 + h = 0
h = 9
For this system to be consistent: h = 9.
Answer: 8 days
Step-by-step explanation:
6 miles has been paved already.
Number of miles left = 30 - 6
= 24 miles
If they are paving at 3 miles a day, the days they will take to finish is:
= 24/3
= 8 days
Answer:
the second description and and expression is correct
Step-by-step explanation:
the first one is wrong because it says 7 minus while it should be minus 7
