SOLUTION: Need help solving system by elimination method x/2 + y/3 = 7/6 2x/3 + 3y/4 = 5/4 Thank you

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Question 1069325: Need help solving system by elimination method
x/2 + y/3 = 7/6
2x/3 + 3y/4 = 5/4

Thank you
Found 3 solutions by Alan3354, Fombitz, rothauserc:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
x/2 + y/3 = 7/6
2x/3 + 3y/4 = 5/4
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I recommend not using fractions if possible.
Less chance of errors.
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Step 1, eliminate fractions.
x/2 + y/3 = 7/6 times 6 --> 3x + 2y = 7
2x/3 + 3y/4 = 5/4 times 12 --> 8x + 9y = 15
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3x + 2y = 7
8x + 9y = 15
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Multiply to make the coefficients of x or y equal.
3x + 2y = 7 times 8 --> 24x + 16y = 56
8x + 9y = 15 times 3 --> 24x + 27y = 45
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24x + 16y = 56
24x + 27y = 45
--------------------------- subtract
-11y = 11
y = -1
================
3x + 2y = 7
3x - 2 = 7
3x = 9
x = 3

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Use the common denominator of 12,
%286%2F12%29x%2B%284%2F12%29y=14%2F12
%288%2F12%29x%2B%289%2F12%29y=15%2F12
Multiply eq. 1 by 9 and subtract from eq. 2 multiplied by 4 to eliminate y,
%2832%2F12%29x%2B%2836%2F12%29y-%2854%2F12%29x-%2836%2F12%29y=60%2F12-126%2F12
-%2822%2F12%29x=-66%2F12
x=3
So,
%286%2F12%293%2B%284%2F12%29y=14%2F12
18%2B4y=14
4y=-4
y=-1

Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
1) x/2 + y/3 = 7/6
2) 2x/3 + 3y/4 = 5/4
:
We can simplify the two equations by multiplying both sides of = in equation 1 by 6 and by multiplying both sides of = in equation 2 by 12
:
3) 3x + 2y = 7
4) 8x + 9y = 15
:
solve equation 3 for x
3x = 7 - 2y
x = (7 - 2y) / 3
:
substitute for x in equation 4
:
8((7- 2y) / 3) + 9y = 15
:
((56 - 16y) / 3) + 9y = 15
:
multiply both sides of = by 3
:
56 - 16y + 27y = 45
11y = -11
y = -1
:
x = (7 - 2*-1) / 3 = 3
:
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x = 3 and y = -1
***********************************
:
check answer by substituting fo x and y in equations 1 and 2
:
equation 1
:
(3 / 2) + (-1 / 3) =
:
(9 / 6) - (2 / 6) = (7 / 6)
:
equation 2
:
(2 *(3 / 3)) + (3 * -1 / 4) =
:
(6 / 3) - (3 / 4) = (8 / 4) - (3 / 4) = (5 / 4)
:
our answer checks
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