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Question 30193: Solve by using the Gaussian elimination method. For instance:
5x+2y=3
3x+4y=13
I seem to always get stuck on the fractions. Please help in details so I know how to solve more problems like this. Thank You.
Answer by ikdeep(226)   (Show Source):
You can put this solution on YOUR website! 5x+2y=3............(1)
3x+4y=13............(2)
For elimination we need one variable in both equation to be equal,,,but here we dnt have that,,,so further solution is done in the following ways...
Multiply (1) by 3 and you get ...
15x + 6y = 9............(3)
Multiply (2) by 5 and you get
15x + 20y = 65............(4)
Now , by elimination method and subtract (4) from (3)and we get...
15x + 6y = 9............(3)
15x + 20y = 65............(4)
- - -
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- 14y = -56 (15x in both eqautions would be eliminated)
or y = -56/-14
y = 4
now, substitute the value of y in any of the equation to get the value of x here I am taking (2)...
3x+4y=13............(2)
putting the values of y = 4 ,,we get
3x + 4 * 4 = 13
3x + 16 = 13
3x = 13 - 16
3x = -3
x = -3/3
x = -1
Now if you wanna verify you answer ,,,you can put the values of x and y in any of the equation and if you get LHS=RHS,,,this means that you answer is correct..
hope this will help you
Please feel free to revert back for any further queries.
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