Answer:
Option C
Step-by-step explanation:
We are given a coefficient matrix along and not the solution matrix
Since solution matrix is not given we cannot check for infinity solutions.
But we can check whether coefficient matrix is 0 or not
If coefficient matrix is zero, the system is inconsistent and hence no solution.
Option A)
|A|=![\left[\begin{array}{ccc}4&2&6\\2&1&3\\-2&3&-4\end{array}\right] =0](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D4%262%266%5C%5C2%261%263%5C%5C-2%263%26-4%5Cend%7Barray%7D%5Cright%5D%20%3D0)
since II row is a multiple of I row
Hence no solution or infinite
OPtion B
|B|=![\left[\begin{array}{ccc}2&0&-2\\-7&1&5\\4&-2&0\end{array}\right] \\=2(10)-2(10)=0](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%260%26-2%5C%5C-7%261%265%5C%5C4%26-2%260%5Cend%7Barray%7D%5Cright%5D%20%5C%5C%3D2%2810%29-2%2810%29%3D0)
Hence no solution or infinite
Option C
![\left[\begin{array}{ccc}6&0&-2\\-2&0&6\\1&-2&0\end{array}\right] \\=2(36-2)=68](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D6%260%26-2%5C%5C-2%260%266%5C%5C1%26-2%260%5Cend%7Barray%7D%5Cright%5D%20%5C%5C%3D2%2836-2%29%3D68)
Hence there will be a unique solution
Option D
![\left[\begin{array}{ccc}5&10&5\\4&1&4\\-1&-2&-1\end{array}\right] \\=2(10)-2(10)=0](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D5%2610%265%5C%5C4%261%264%5C%5C-1%26-2%26-1%5Cend%7Barray%7D%5Cright%5D%20%5C%5C%3D2%2810%29-2%2810%29%3D0)
=0
(since I row is -5 times III row)
Hence there will be no or infinite solution
Option C is the correct answer
Answer:
a) 4 people ordered streak dinner
b) 3 people ordered chicken dinner
Step-by-step explanation:
Let the number of people that ordered steak dinner be x
and the number of people that ordered chicken dinner be y
From the question,
There are 7 people in your family
Hence, we can write that
x + y = 7 ...... (1)
Also from the question
Some order the chicken dinner for $13 and some order the steak dinner for $18 and the total bill was $111.
We can then write that
13y + 18x = 111 ...... (2)
From equation (1)
x + y = 7
Then,
x = 7 - y ...... (3)
Put this into equation (2)
13y + 18x = 111
13y + 18(7 - y) = 111
13y + 126 - 18y = 111
-5y = -15
5y = 15
y = 15 / 5
y = 3
Put the value of y into equation (3) to get x
x = 7 - y
Then
x = 7 - 3
x = 4
Hence, 4 people ordered streak dinner
and 3 people ordered chicken dinner
a) 4 people ordered streak dinner
b) 3 people ordered chicken dinner
Answer:
D
Step-by-step explanation:
X-y=2 (*-2) --> -2x+2y=-4
2x+3y=14
------------------
2x+3y=14
-2x+2y=-4
------------------
5y=10
y=2
Answer:
Angle 2: 110 degrees, 1 and 2 would have to be the same for the lines to be parallel
Angle 3: 70 degrees angle 3 would have to be the complement to angle 1, so 1+3=180 and 70*3=180, so 3=70 degrees
Angle 4: 70 degrees, 3 and 4 have to be the same opposite angles for the lines to be parallel
