Answer: The system of equations is:
x + 2y + 2 = 4
y - 3z = 9
z = - 2
The solution is: x = -22; y = 15; z = -2;
Step-by-step explanation: ONe way of solving a system of equations is using the Gauss-Jordan Elimination.
The method consists in transforming the system into an augmented matrix, which is writing the system in form of a matrix and then into a <u>Row</u> <u>Echelon</u> <u>Form,</u> which satisfies the following conditions:
- There is a row of all zeros at the bottom of the matrix;
- The first non-zero element of any row is 1, which called leading role;
- The leading row of the first row is to the right of the leading role of the previous row;
For this question, the matrix is a Row Echelon Form and is written as:
![\left[\begin{array}{ccc}1&2&2\\0&1&3\\0&0&1\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%262%262%5C%5C0%261%263%5C%5C0%260%261%5Cend%7Barray%7D%5Cright%5D)
![\left[\begin{array}{ccc}4\\9\\-2\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D4%5C%5C9%5C%5C-2%5Cend%7Barray%7D%5Cright%5D)
or in system form:
x + 2y + 2z = 4
y + 3z = 9
z = -2
Now, to determine the variables:
z = -2
y + 3(-2) = 9
y = 15
x + 30 - 4 = 4
x = - 22
The solution is (-22,15,-2).
Answer:
It's 104 1/4
Step-by-step explanation:
He is correct and incorrect. 2 and 4 can create factors but they can also be factors of other numbers. So 8 can be a factor of bigger whole numbers and can also have it own smaller factors.
Answer:
Here's a picture of the answer.
Step-by-step explanation:
Let Y = total cost of both schools.
The total cost would be ( number of credits at Westside x 98) + (number of credits at Pinewood x 115).
The total number of credits he is taking is 14.
If w is the number of credits at Westside, then for Westside you have 98w ( $98 times the number of credit hours)
The equation is now y = 98w + (number of credits at Pinewood x 115).
The number of credit hours at Pinewood would be the total credit hours 14 minus the credit hours at Westside w, so you have 14-w, which needs to be multiplied by the cost at Pinewood.
The equation is now y = 98w + 115(14-w)
This can be simplified using the distributive property to:
Y = 98w + 1610 - 115w
Y = -17w + 1610
