Step-by-step explanation:
Given
One plain pizza and two sodas cost $15.95
Similarly, 3 plain pizzas and 5 sodas cost $45.90
Suppose the cost of single pizza and soda be
and 
In linear equation format, it can be written as

Therefore, the above two equations represents the given situation.
Answer: β ≠ ±1
Step-by-step explanation: For a system of equations to have an unique solution, its determinant must be different from 0: det |A| ≠ 0. So,
det
≠ 0
Determinant of a 3x3 matrix is calculated by:
det ![\left[\begin{array}{ccc}1&\beta&1-\beta\\2&2&0\\2-2\beta&4&0\end{array}\right]\left[\begin{array}{ccc}1&\beta\\2&2\\2-2\beta&4\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%26%5Cbeta%261-%5Cbeta%5C%5C2%262%260%5C%5C2-2%5Cbeta%264%260%5Cend%7Barray%7D%5Cright%5D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%26%5Cbeta%5C%5C2%262%5C%5C2-2%5Cbeta%264%5Cend%7Barray%7D%5Cright%5D)
![8(1-\beta)-[2(2-2\beta)(1-\beta)]](https://tex.z-dn.net/?f=8%281-%5Cbeta%29-%5B2%282-2%5Cbeta%29%281-%5Cbeta%29%5D)




β ≠ ±1
For the system to have only one solution, β ≠ 1 or β ≠ -1.
Answer:
Therefore the greatest number of cookies she can put each bag is 14.
Step-by-step explanation:
Given that Anna has made 30 chocolate chip cookies and 54 sugar cookies.
First we have to find out the number of fried or the number of bags.
So to find the number of bags, We need to find out the G.C.D of 30 and 54.
30=5×3×2
54=3×3×3×2
The common divisor of 30 and 54 is = 3×2 = 6
∴The G.C.D of 30 and 54 is 6.
The number of bags is 6.
The number of chocolate cookies each bags is
=(The number of chocolate cookies÷ 6)
=30÷6
=5
The number of sugar cookies each bags is
=(The number of sugar cookies÷ 6)
=54÷6
=9
Therefore the greatest number of cookies she can put each bag is (5+9)=14.
The answer to your question is 64.