n(A) = 26
Solution:
Let us first define the cardinal number of the set.
Cardinal number of the set:
The number of distinct elements in a finite set is called its cardinal number. It is denoted as n(A).
Given set: A = {a, b, c, .... z}
We know that, there are 26 elements in the alphabet "a to z".
Number of elements in the set A = 26
Hence n(A) = 26.
Here you have to find which each variable is, for this you start of picking one equation,
x + 2y + 6z = 4
-3x + 2y - 2 = -4
4x + 2z = 16
depending the equation you pick you multiply that by a certain number that will give you the opposite of one of the other equations,
-1(x + 2y + 6z = 4)
= -x -2y - 6z = -4
With this you add or subtract it with the equation that has the same number or variable, or both,
In this case it will be the equation,
-3x + 2y + 6z = 4
You can use this one or the third equation since both have a positive 2y which will cancel with -2y from the new equation,
-x - 2y - 6z = -4
-3x + 2y -z = -4
= -4x -7z = -8
Now you since you just eliminated the variable (y) you now have 2 variables, and the last equation has only 2 variables, meaning now you find the answer to those to equations,
-4x -7z = -8
4x + 2z = 16
= -5z = 8
Now leave the variable by itself,
z = 8/5
Now you found the variable (z), with this just substitute on one of the equations we used to find (z) so you can find (x), after that substitute those answered to on of the original equations so you can find (y)
7. 20
8. 680
9. 700
10. 4,000
11. 106,000
12. 5,800
The simplified form is C .
