Solve 1/2(2x+3y) + 12/7(3x-2y) =1/2 7/2x-3y +4/3x-2y =2 where (2x+3y) and (3x-2y) is not equal to 0
Answers
1/2(2x+3y)+12/7(3x-2y)=1/2
7/(2x+3y)+4/(3x-2y)=2
Let 1/(2x+3y)=u & 1/(3x-2y)= v
Then the given system of equations becomes
u/2 + 12v/7 = 1/2
(7u + 12×2v) / 14 = 1/2
(7u + 24v) = (1/2) × 14
7u +24v = 7 ............ (1)
7u + 4v = 2 ............. (2)
By Subtracting equation 2 from equation 1.
7u +24v = 7
7u + 4v = 2 [elimination method]
(-) (-) (-)
_____________
20 v = 5
v = 5/20 = 1/4
By Putting v = 1/4 in equation 1.
7u +24v = 7
7u + 24 (1/4) =7
7u + 6= 7
7u = 7-6
7u = 1
u = 1/7
Now, u = 1/7 = 1/(2x+3y)
(2x+3y) = 7 ...................... (3)
v = 1/4 = 1/(3x-2y)
(3x-2y) = 4 ....................... (4)
Multiply equation 3 by 2 an equation 4 by 3,
4x + 6y = 14 .................... (5)
9x - 6y = 12...................... (6)
Adding Equations 5 and 6,
4x + 6y = 14
9x - 6y = 12
_________
13x = 26
x= 26/13
x= 2
Putting x= 2 in question 5,
4x + 6y = 14
4(2) + 6y = 14
8 + 6y = 14
6y = 14 - 8
6y = 6
y = 6/6
y = 1
Hence,
x = 2,y = 1 is the solution of the given system of equations.
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