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x/2+y/3=7 ----(1)
x/4+2y/3=8 ----(2)
In (1) the dr quantities on the LHS are 2 and 3.
And the lcm of 2 and 3 is 6
Therefore multiply (1) throughout by 6
which gives 3x+2y = 42 ----(3)
In (2) the dr quantities on the LHS are 4 and 3.
And the lcm of 4 and 3 is 12
Therefore multiply (2) throughout by 12
which gives 3x+8y = 96 ----(4)
Observe that the coefficients of x in both (3) and (4) are equal
Therefore (3) - (4) should get rid of the x variable.
(3) - (4) implies
(3x-3x)+(2y-8y)= (42-96)
0-6y = -54
-6y = -54
Therefore y = (-54)/(-6) = +9
x = 9 in 3x+2y = 42 ----(3)
gives 3x+(2X9)=42
3x+18 = 42
3x=42-18
3x=24
x=24/3 = 8
Answer: x=8 and y=9
Verification: Putting x=8 and y=9 in x/4+2y/3=8 ----(2)
LHS = x/4+2y/3= 8/4+(2X9)/3 = 2+6 = 8 =RHS
Therefore our values are correct
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