4C =2A + 2B , 2B = A + 3C How many C's will balance the combination of A and B
4C = 2A + 2B ----> C = (2A+2B)/4
2B = A+3C ------> C = (2B-A)/3
(2A + 2B)/4 = (2B-A)/3
6A + 6B = 8B - 4A
10A = 2B
B = 5A
into C = (2A+2B)/4
C = (2A + 10A)/4
C = 3A
etc
Solve the set of linear equations by the matrix method : a+3b+2c=3 , 2a-b-3c= -8, 5a+2b+c=9. Sove for c
To determine how many C's will balance the combination of A and B, we need to solve the given equations.
Let's start by substituting the value of 2B from the second equation into the first equation:
4C = 2A + (A + 3C)
Simplify the equation:
4C = 2A + A + 3C
Combine like terms:
4C - 3C = 2A + A
C = 3A
Now we have an expression for C in terms of A. To balance the combination of A and B, we need C to be equal to the sum of A and B.
C = A + B
Substitute the value of C we found earlier:
3A = A + B
Subtract A from both sides:
3A - A = B
2A = B
So, to balance the combination of A and B, the number of Cs should be twice the number of As.