Question

Solve for x and y :

[9/3x+8y] + [7/8x−3y] = 41

[5/3x+8y] - [7/8x−3y] = 1

[NOTE: Give your answer correct up to 2 decimal places]

Answer 1

[9/(3x+8y)] + [7/(8x-3y)] = 41

[5/(3x+8y)] - [7/(8x-3y)] = 1

Let,   1/(3x+8y) = a    and   1/(8x-3y) = b

So, now the equations look like this......

9a + 7b = 41 ------------- equation 1

5a - 7b = 1 --------------- equation 2

Solve them to get the values of a and b.....

9a  +  7b =  41

5a  -  7b =   1

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14a - 0 = 42

14a = 42

a = 3

Now,put this value to either equation 1 or equation 2 to get value of b...

9a + 7b = 41

9(3) + 7b = 41

7b = 41 - 27

7b = 14

b = 2

NOW, THE LAST PART..........................

Put these values of 'a' and 'b' in this.........

1/(3x+8y) = a    and   1/(8x-3y) = b

1/(3x+8y) = 3    and   1/(8x-3y) = 2

9x + 24y = 1     and    16x - 6y = 1

9x + 24y = 1 --------------*6

16x - 6y = 1  --------------- *24

54x   + 144y = 6 ---------------    equation 3

384x - 144y = 24  -------------- equation 4

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438x - 0 =       30

438x = 30

x = 30/438

x = 0.06

54x   + 144y = 6

54(30/438)   + 144y = 6

144y = 6 - 3.69

144y = 2.31

y = 0.01