Answer:
<em>A prime number is a whole number greater than 1 whose only factors are 1 and itself</em>
two is the only even prime number because it is divisible by only two and one. All the other even numbers are not prime because they are all divisible by two.
4 bowls of pasta would be served for twelve people.
4×3=12
Answer:
The solution to the equation system given is:
- <u>x = 2</u>
- <u>y = -1</u>
Step-by-step explanation:
First, we must know the equations given:
- 2x + 3y = 1
- 3x + y = 5
Following Crammer's Rule, we have the matrix form:
![\left[\begin{array}{ccc}2&3\\3&1\end{array}\right] =\left[\begin{array}{ccc}x\\y\end{array}\right] = \left[\begin{array}{ccc}1\\5\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%263%5C%5C3%261%5Cend%7Barray%7D%5Cright%5D%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx%5C%5Cy%5Cend%7Barray%7D%5Cright%5D%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%5C%5C5%5Cend%7Barray%7D%5Cright%5D)
Now we solve using the determinants:
![x=\frac{\left[\begin{array}{ccc}1&3\\5&1\end{array}\right]}{\left[\begin{array}{ccc}2&3\\3&1\end{array}\right] } =\frac{(1*1)-(5*3)}{(2*1)-(3*3)} = \frac{1-15}{2-9} =\frac{-14}{-7} = 2](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%263%5C%5C5%261%5Cend%7Barray%7D%5Cright%5D%7D%7B%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%263%5C%5C3%261%5Cend%7Barray%7D%5Cright%5D%20%7D%20%3D%5Cfrac%7B%281%2A1%29-%285%2A3%29%7D%7B%282%2A1%29-%283%2A3%29%7D%20%3D%20%5Cfrac%7B1-15%7D%7B2-9%7D%20%3D%5Cfrac%7B-14%7D%7B-7%7D%20%3D%202)
![y=\frac{\left[\begin{array}{ccc}2&1\\3&5\end{array}\right]}{\left[\begin{array}{ccc}2&3\\3&1\end{array}\right] } =\frac{(2*5)-(3*1)}{(2*1)-(3*3)}=\frac{10-3}{2-9} =\frac{7}{-7}=-1](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%261%5C%5C3%265%5Cend%7Barray%7D%5Cright%5D%7D%7B%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%263%5C%5C3%261%5Cend%7Barray%7D%5Cright%5D%20%7D%20%3D%5Cfrac%7B%282%2A5%29-%283%2A1%29%7D%7B%282%2A1%29-%283%2A3%29%7D%3D%5Cfrac%7B10-3%7D%7B2-9%7D%20%3D%5Cfrac%7B7%7D%7B-7%7D%3D-1)
Now, we can find the answer which is x= 2 and y= -1, we can replace these values in the equation to confirm the results are right, with the first equation:
- 2x + 3y = 1
- 2(2) + 3(-1)= 1
- 4 - 3 = 1
- 1 = 1
And, with the second equation:
- 3x + y = 5
- 3(2) + (-1) = 5
- 6 - 1 = 5
- 5 = 5
Answer:
The answer just so happens to be 6!
Elaborate what do the symbols stand for pmme if you need more help.