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 ![\left[\begin{array}{ccc}1&\beta&1-\beta\\2&2&0\\2-2\beta&4&0\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)
≠ 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.
The answer to this problem is x> -64
Answer:
D. The rate of change for function B is greater than the rate of change for function A
Step-by-step explanation:
Function a has a slope (aka rate of change) of 3/3
I know this because we start at (-3, 0) then finish at (0, 3)
We added 3 to both the x value and the y value.
3/3 = 1, so we have a rate of change of 1 for function A
Now that we know this, we can write the equation out into slope intercept form.
We can get y = x + 3
The equation for function B is y = 5x + 5
The slope for function B is greater, therefore the rate of change for function B is greater than the rate of change for function A
the system has no solution.
Option C is correct.
Step-by-step explanation:
We need to solve the system of equations by substitution
Putting value of x from eq(2) into eq(1)
As as 0≠4is not true, we cannot find the value of y so the system has no solution.
Option C is correct.
Keywords: System of equations
Learn more about system of equations at:
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Hi,
The greatest common factor of 30 and 50 is 10.
Have a great day!
