Question 54398: I am having trouble understanding system of equations. i have tried to work the problem out but im not sure what steps to take. can you help me on the problem 3x/2 + y/4=7
x/5 - 2y/3 = 2 1/3
Found 3 solutions by Edwin McCravy, stanbon, Earlsdon:
Answer by Edwin McCravy(20056)   (Show Source):
You can put this solution on YOUR website! I am having trouble understanding system of equations.
i have tried to work the problem out but im not sure what
steps to take. can you help me on the problem
3x/2 + y/4 = 7
x/5 - 2y/3 = 2 1/3
We need to clear fractions in each equation:
Put the the 7 of the first equation over 1 so everything
will be a fraction:
3x y 7
---- + --- = ---
2 4 1
Multiply every term by the LCD of 3 and 4, which is 12.
Put it over 1 too:
12 3x 12 y 12 7
----·---- + ----·--- = ----·---
1 2 1 4 1 1
Cancel the 2 into the 12 in the first term, getting 6.
Cancel the 4 into the 12 in the second term, getting 3.
6 3
12 3x 12 y 12 7
----·---- + ----·--- = ----·---
1 2 1 4 1 1
1 1
All that's left is
18x + 3y = 84
------------------------
x/5 - 2y/3 = 2 1/3
Change the 2 1/3 to a mixed fraction 7/3
x/5 - 2y/3 = 2 1/3
x 2y 7
--- - ---- = ---
5 3 3
Multiply every term by the LCD of 5, 3 and 3, which is 15.
Put it over 1 too:
15 x 15 2y 15 7
----·--- - ----·---- = ----·---
1 5 1 3 1 3
Cancel the 5 into the 15 in the first term, getting 3.
Cancel the 3 into the 15 in the second term, getting 5.
Cancel the 3 into the 15 in the term on the right,
getting 5
3 5 5
15 x 15 2y 15 7
----·--- - ----·---- = ----·---
1 5 1 3 1 3
1 1 1
All that's left is
3x - 10y = 35
-----------------------------------------------
Now you have the fractionless system
18x + 3y = 84
3x - 10y = 35
Can you solve that system? If not post again.
Answer: (x, y) = (5, 2)
Edwin
Answer by stanbon(75887)  (Show Source):
You can put this solution on YOUR website! 1st:3x/2 + y/4=7
Multiply thru by 4 to get:
2nd: 6x+y=28
3rd: x/5 - 2y/3 = 2 1/3
Multiply thru by 15 to get:
4th: 3x-19y=35
To eliminate the "x" terms multiply thru 4th by 2 to get:
5th: 6x-38y=70
Subtract 5th from 2nd to get:
6th: 39y=-42
Then y=-14/13
Substitute that into 2nd to solve for "x":
6x-14/13 = 28
6x=14/13 + 364/13
6x = 378/13
x= 63/13
Solution:
x=63/13 y=-14/13
cheers,
Stan H.
Answer by Earlsdon(6294) (Show Source):
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