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Answers
Answer:
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Step-by-step explanation:
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 + 12x2v) / 14= 1/2
(7u + 24v) = (1/2) × 14
7u + 24 v = 7............(1)
7u + 4v = 2................(2)
Subtracting equation 2 from eq 1.
7u +24v = 7
7u +4v. = 2 [Elimination Method]
(-) (-) (-)
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20v = 5
v=1/4
Putting v 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 and equation 4 by 3,
4x + 6y = 14............(5)
9x - 6y = 12.............(6)
Adding Equations 5 and 6,
4x + 6y = 14
9x - 6y =12
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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= 1
Hence, x= 2 ,y= 1 is the solution of the given system of equations.
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