Question

5x-2y-8=0
2x-5y-12=0
find x&y​

Answer 1

Answer:

1. 5x - 2y - 8 = 0 -------------------------------- (i)

2. 2x - 5y - 12 = 0 -------------------------------(ii)

Now, in eq(i) ,

     5x - 2y - 8 = 0

  => 5x = 8 + 2y

  => x = (8+ 2y ) /5 ---------------------------------(iii)

Now putting  the value of x from eq(III) in eq(ii), we get,

     2x - 5y - 12 = 0

  => 2[( 8 + 2y )/5] - 5y = 12

  => [(16 + 4y) /5 ] - 5y = 12

  => 16 + 4y - 25y = 60

  => -21y = 44

  => y = -44/21 --------------------------------------------- (iv)

Now ,

  putting the value of y in eq(iii), we get

          x = [8 + 2 ( -44/21 )]/5

        => x = (168 - 88)/105

        => x = 80/105

        => x = 16/21

∴ x = 16/21 and y = -44/21   (Ans.)

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Answer 2

$\tt\red{SOLUTION:-}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \:$

$\tt{5x - 2y - 8 = 0}$

$\tt{5x - 2y = 8 - - - - - - - eq(1)}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \:$

$\tt{2x - 5y - 12 = 0}$

$\tt{2x - 5y = 12 - - - - - - eq(2)}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \:$

$\tt\red{ MULTIPLY \: 2 × Eq(1) \: AND \: 5 × Eq (2)}$

$\tt{2(5x - 2y = 8 )}$

$\tt{10x - 4y = 16 - - - - - - eq(3)}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \:$

$\tt{5(2x - 5y = 12) }$

$\tt{10x - 25y = 60 - - - - - eq(4) }$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \:$

$\tt\red{NOW \: USE \: ELIMINATION \: METHOD}$

$\tt{10x - 4y = 16}$

$\tt{10x - 25y = 60 }$

$- \: \: \: \: \: \: \: + \: \: \: \: \: \: \: \: \: \: -$

$\tt{21y = - 44}$

$\tt \red{y = \frac{ - 44}{21} }$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \:$

$\tt\red{IN \: EQ(1) }$

$\tt{5x - 2y = 8}$

$\tt{5x - 2 \times \frac{ - 44}{21} = 8}$

$\tt{5x + \frac{ 88}{21} = 8}$

$\tt{5x = 8 - \frac{ 88}{21}}$

$\tt{5x = \frac{168}{21} - \frac{ 88}{21}}$

$\tt{5x = \frac{ 80}{21}}$

$\tt{x = \frac{ 80}{21} \times \frac{1}{5} }$

$\tt \red{x = \frac{16}{21} }$