Question

Solve for x and y
1/2(x+3y)+5/3(3x-2y)=-3/2
5/4(x+2y)-3/5(3x-2y)=61/60

Answer 1

1/2(x+3y)+5/3(3x-2y)=-3/2 let it is first equation 
=x/2+3y/2 + 5x-10y/3=-3/2
11x/2 - 11/6y=-3/2
multiply this equation by 6
33x-11y=-9  let this is equation 1 
5/4(x+2y)-3/5(3x-2y)=61/60 let this equation is 2nd equation
5/4x +5/2y - 9/5x-6/5y=61/60 
(25x-36x)/20 + (25y-12y)/10 = 61/60
multiply this equation by 60
3(-11x)  + (13y)6=61
-33x+78y=61 let this eqution is second equation 
33x-11y=-9
-33x+78y=61
add these two eqution 
0+68y=52
y=68/52 put the value of y in 1st equation 
33x-11y=-9 
33x-11(68/52)=-9
33x-748/52=-9
33x*52-748=-9*52
1716x =-468+748
1716x=300
x=300/1716

Answer 2

1/2(x+3y) + 5/3(3x-2y) = -3/2
x/2 + 3y/2 + 15x/3 - 5y/3 = -3/2
33x - y = -9.............(1)
5/4(x+2y) - 3/5(3x-2y) = 61/60
-11x + 74y = 61/3.................(2)
From eq. 1 y = 9 + 33x
From eq. 2 y = 61 - 33x / 222
THEREFORE, 9 + 33x = 61 -33x / 222 {method of similarity}

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