Answer:
I would choose either A.x 22 or D. infinitely many solutions
Step-by-step explanation:
Since you did put the answer choice B then I don't know what are all the possible answer choices
Answer:
The correct option is (A).
Step-by-step explanation:
If the reduced row echelon form of the coefficient matrix of a linear system of equations in four different variables has a pivot, i.e. 1, in each column, then the reduced row echelon form of the coefficient matrix is say A is an identity matrix, here I₄, since there are 4 variables.
![\left[\begin{array}{cccc}1&0&0&0\\0&1&0&0\\0&0&1&0\\0&0&0&1\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D1%260%260%260%5C%5C0%261%260%260%5C%5C0%260%261%260%5C%5C0%260%260%261%5Cend%7Barray%7D%5Cright%5D)
Then the corresponding augmented matrix [ A|B] , where the matrix is the representation of the linear system is AX = B, must be:
![\left[\begin{array}{ccccc}1&0&0&0&a\\0&1&0&0&b\\0&0&1&0&c\\0&0&0&1&d\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccccc%7D1%260%260%260%26a%5C%5C0%261%260%260%26b%5C%5C0%260%261%260%26c%5C%5C0%260%260%261%26d%5Cend%7Barray%7D%5Cright%5D)
Now the given linear system is consistent as the right most column of the augmented matrix is a linear combination of the columns of A as the reduced row echelon form of A has a pivot in each column.
Thus, the correct option is (A).
Answer:
Step-by-step explanation:
c.d. d=11-18=4-11=-7
y=18+(n-1)(-7)
or y=18-7n+7
or y=25-7n
n=1,2,3, ...
Answer:
79 sociology textbooks and 138 biology textbooks
Step-by-step explanation:
Create a system of equations, where b is the number of biology books and s is the number of sociology books:
b + s = 217
b = s + 59
Solve by substitution by substituting s + 59 for b into the first equation:
b + s = 217
s + 59 + s = 217
Add like terms and solve for s:
2s = 158
s = 79
So, there were 79 sociology books. To find the number of biology books, substitute 79 in for s into the equation b = s + 59
b = s + 59
b = 79 + 59
b = 138
So, 79 sociology textbooks and 138 biology textbooks were sold.