SOLUTION: Please help! I can not figure out two problems. I am to determine whether the following system is consistent, inconsistent, or dependent. If the system is consistent, find the solu

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Please help! I can not figure out two problems. I am to determine whether the following system is consistent, inconsistent, or dependent. If the system is consistent, find the solu      Log On


   

Question 4561: Please help! I can not figure out two problems. I am to determine whether the following system is consistent, inconsistent, or dependent. If the system is consistent, find the solution of the system.
The first problem is :
6x + 4y =8
9x + 6y =12

and the second problem is:
2/3x + 3/4y =4
5/6x - 3/8y = -11/2

Answer by Abbey(339) About Me  (Show Source):
You can put this solution on YOUR website!
6x + 4y =8
9x + 6y =12
Multiply the second equation by 2/3:
6x + 4y = 8
6x + 4y = 8
These are identical so they are the same line!
Second problem:
2x%2F3+%2B+3y%2F4+=4
5x%2F6+-+3y%2F8+=+-11%2F2
Since I don't want to work with fractions, I will:
Multiply the first equation by 12 to clear the denominators
Multiply the second equation by 24 to clear the denominators
8x + 9Y = 48
20x- 9y = -132
Add them together:
28x = -84
Divide both sides by 28:
x=3
substitute back into either equation:
2%283%29%2F3+%2B+3y%2F4+=4
Clear parentheses:
2%2B+3y%2F4+=+4
subtract 2 from each side:
3y%2F4+=+2

Multiply both sides by 4/3:
y=8%2F3

check by putting x and y back into the second equation to validate:
5x%2F6+-+3y%2F8+=+-11%2F2
5%283%29%2F6-%283%2F8%29%2A%288%2F3%29=-11%2F2
5%2F2-1=-11%2F2
5%2F2-2%2F2=-11%2F2
this is not a true statement, so this problem has no solution.