1/2(x+2y) +5/3(x-2y)=-3/2 ,5/4(x+2y)- 3/5(3x-2y)=61/60

Asked by samridhi arora | 1st Jul, 2013, 05:31: PM

Expert Answer:

Please note that your first equation should be 1/2(x+2y) +5/3(3x-2y)=-3/2
Let x + 2y = u and 3x-2y = v
 
So, the equations would become
1/2u+5/3v =-3/2 and 5/4u- 3/5v=61/60  
Taking LCM
 
3u + 10v = -9 and 25u - 12v = 61/3
Multiplying the first equation by 25 and second by 3
75u + 250v = -225 and 75u -36v = 61
now subtracting the 2 equations
250v - (-36v) = -225 - 61
286v = -286
v = -1
u = -9-10(-1)/3 = 1/3 
 
Now, x + 2y = 1/3 and 3x-2y = -1
Adding the 2 equations
4x = -2/3
x = -1/6
 
and 2y = 1/3-(-1/6) = 1/2
y = 1/4


Answered by  | 1st Jul, 2013, 10:44: PM

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