SOLUTION: I am so confused...I need to solve each system by the addition method, I am only understanding half of the process. {{{1/4X + 1/3y = 5}}} {{{x - y = 6}}}

Algebra ->  Linear-equations -> SOLUTION: I am so confused...I need to solve each system by the addition method, I am only understanding half of the process. {{{1/4X + 1/3y = 5}}} {{{x - y = 6}}}      Log On


   

Question 124548: I am so confused...I need to solve each system by the addition method, I am only understanding half of the process.
1%2F4X+%2B+1%2F3y+=+5
x+-+y+=+6
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
1%2F4X+%2B+1%2F3y+=+5
x+-+y+=+6
:
Are you sure you have this problem written correctly? Could it be:
1%2F4x + 1%2F3y = 5
:
GEt rid of the denominators by multiplying equation by 12
12*1%2F4x + 12*1%2F3y = 12(5)
:
Cancel the denominators and you have:
3x + 4y = 60
:
Multiply the 1st equation (x-y=6), by 4 and add to the above equation
3x + 4y = 60
4x - 4y = 24
---------------- adding eliminates y
7x + 0y = 84
7x = 84
x = 84%2F7; divided both sides by 7
x = 12
:
Find y using x - y = 6; substitute 12 for y
12 - y = 6
-y = 6 - 12
-y = -6
y = +6; multiplied equation by -1 to get rid of the negatives
:
Now let's check our solutions in the original equations:
1%2F4*12 + 1%2F3*6 = 5
3 + 2 = 5; confirms our solution
:
:
Did this unconfuse you? Any questions?