Question

Solve by Elimination by Substitution method and find the value of 2x + y

5.)
$\frac{1}{2(2 + 3y)} + \frac{12}{7(3x - 2y)} = \frac{1}{2}$
;
$\frac{7}{(2x + 3y)} + \frac{4}{(3x - 2y)} = 2$

Ans: 2 , 1 ; 5

Standard:- 10

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Answer 1

Heya !!!

1 / 2 ( 2X + 3Y ) + 12 / 7 ( 3X - 2Y ) = 1/2 --------(1)

And,

7 / ( 2X + 3Y ) + 4/ (3X - 2Y ) = 2 --------(2)

Putting 1/ ( 2X + 3Y ) = U and 1/ ( 3X - 2Y ) = V , the given equations become

U/2 + 12V/7 = 1/2

7U + 24V = 7 -----------(3)

And,

7U + 4V = 2 ------(4)

Subtracting equation (4) from equation (3) ,

7U + 24V = 7
7U + 4V = 2
------------------

20V = 5

V = 5/20 = 1/4

Putting V = 1/4 in equation (3) , we get

7U + 24V = 7

7U + 24 × (1/4) = 7

7U + 6 = 7

7U = 1

U = 1/7

Now,

U = ( 1/2X + 3Y )

1/7 = 1/2X + 3Y

2X + 3Y = 7 ----------(5)

And,

V = ( 1/3X - 2Y )

1/4 = (1/3X - 2Y )

3X - 2Y = 4 -------(6)

Multiply equation (5) by 2 and equation (6) by 3 , we get

4X + 6Y = 14 --------(7)

And,

9X - 6Y = 12 ----------(8)

Adding equation (7) and equation (8) we get

4X + 9X = 14 + 12

13X = 26

X = 26/13 = 2

Putting X = 2 in equation (5) , we get

2X + 3Y = 7

( 2 × 2 ) + 3Y = 7

3Y = (7-4)

Y = 3/3 = 1


★ X = 2 and Y = 1.

Therefore,

2X + Y = 2 × 2 + 1 = 5.

★ HOPE IT WILL HELP YOU ★

Answer 2

3x - 2(1) = 4

3x - 2 = 4

3x = 6

x = 6/3

x= 2







Hence,

2x + 1

2(2) + 1

4 + 1

=> 5



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