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

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) (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:

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:

Clear parentheses:

subtract 2 from each side:

Multiply both sides by 4/3:

check by putting x and y back into the second equation to validate:

this is not a true statement, so this problem has no solution.

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