SOLUTION: Using elimination method what is x and y in the equation: 2x/3 + y/6 = 1 x/6 - y/2 = 1

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Question 1108061: Using elimination method what is x and y in the equation:
2x/3 + y/6 = 1
x/6 - y/2 = 1
Found 2 solutions by Alan3354, rothauserc:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!

2x/3 + y/6 = 1
x/6 - y/2 = 1
================
Multiply by 6 to eliminate fractions.
4x + y = 6
x - 3y = 6
------
Multiply the 1st eqn by 3
12x +3y = 18
x - 3y = 6
------------------- Add
13x = 24
x = 24/13
y = -18/13

Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
1) 2x/3 + y/6 = 1
:
2) x/6 - y/2 = 1
:
rewrite equations 1 and 2 using the least common multiple of the divisors
:
3) 4x + y = 6
:
4) x - 3y = 6
:
multiply equation 3 by 3
:
5) 12x + 3y = 18
:
add equation 5 and equation 4
:
13x = 24
x = 24/13
:
use equation 2 to solve for y
:
(24/13) * (1/6) - y/2 = 1
:
(4/13) - y/2 = 1
:
-y/2 = 9/13
:
y = -18/13
:
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x = 24/13 and y = -18/13
:
check answer with equation 1
:
(2/3) * (24/13) + (1/6) * (-18/13) = 1
:
(16/13) - (3/13) = 1
:
1 = 1
:
check answer in equation 2
:
(1/6) * (24/13) - (1/2) * (-18/13) = 1
:
(4/13) + (9/13) = 1
:
1 = 1
:
answer checks
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