SOLUTION: Can you help-- Solve the system by the addition method. x/3-y/2=-5/6, x/5-y/3=-3/5 Thank you all

Question 194216: Can you help-- Solve the system by the addition method.
x/3-y/2=-5/6, x/5-y/3=-3/5
Thank you all

Answer by anantha(86) (Show Source): You can put this solution on YOUR website!
sol:x/3-y/2= -5/6 this is the 1st equation
take l.h.s part the l.c.m of 3,2 is 6
multiplying by 6 on both sides of the equation
(x/3)*6-(y/2)*6= -(5/6)*6
2x-3y= -5 --------(3 equation)
x/5-y/3= -3/5
take l.h.s part the l.c.m of 5,3 is 15
multiplying both sides by 15
(x/5)*15-(y/3)*15= (-3/5)*15
3x-5y=-7 --------(4 th equation)
solving these two equations we get x,y values
2x-3y= -5
3x-5y=-7
multiplying 3 equation by 3 on both sides and multiplying 4th equation by 2 on both sides
2x*3-3y*3= -5*3
3x*2-5y*2= -7*2

6x-9y= -15
6x-10y=-14
on solving these equations changin the symbols of 2nd equation
6x-9y= -15
-6x+10y= +14
--------------------
0+1y= -1
y= -1
substitute this value in 3rd equation we get x value
2x-3y= -5
2x-3*(-1)= -5
2x+3= -5
subtracting 3 on both sides
2x+3-3= -5-3
2x=-8
dividing by 2 on both sides
2x/2= -8/2
x= -4
check these values correct or not
substitute these values in 3rd equation
2x-3y= -5
2*(-4)-3*(-1)= -5
-8+3=-5
-5= -5
these two values satisfy the equations

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