Question

Solve 4x-2y=9, 3x+4y=4 by elimination method

Answer 1

$\textbf{Answer :}$

The given equations are

4x - 2y = 9 ...(i)
3x + 4y = 4 ...(ii)

Now, multiplying (i) by 3 and (ii) by 4, we get

12x - 6y = 27
12x + 16y = 16

On subtraction, we get

- 6y - 16y = 27 - 16

=> - 22y = 11

=> y = -1/2

Putting y = -1/2 in (i), we get

4x - 2 (-1/2) = 9

=> 4x + 1 = 9

=> 4x = 9 - 1

=> 4x = 8

=> x = 2

Therefore, the required solution be

x = 2 and y = -1/2

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Answer 2

4x - 2y = 9

4x - 9 = 2y

(4x - 9)/2 = y ----1equation

Then,

3x + 4y = 4

Putting the value of y from 1equation

3x + 4(4x-9)/2 = 4

3x + 8x - 18 = 4

11x = 4+18

11x = 22

x = 22/11

x = 2

Then, putting the value of x from 1equation,

[4x - 9] / 2 = y

[ 4(2) - 9] / 2 = y

[ 8 - 9] /2 = y

-1/2 = y


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METHOD 2,

4x - 2y = 9 ---1equation
3x + 4y = 4 ---2equation


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[ 4x - 2y = 9] × 4
[ 3x + 4y = 4] × 2

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16x - 8y = 36 --3equation
6x + 8y = 8 ---4equation

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Adding (3) & (4),

16x + 8y = 36
6x - 8y = 8
___________
22x = 44
___________

x = 44/22

x = 2

Putting the value of x in 2equation,

3x + 4y = 4

3(2) + 4y = 4

6 + 4y = 4

6 - 4 = -4y

2 = -4y

-2/4 = y

-1/2 = y


I hope this will help you

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