1.

4x - 3y - 18 = 0; 4y - 5x -7 = 0..solve the linear equation ​

Answer»

Answer :

x = 93 and y = 118

Step-by-step explanation :

GIVEN linear equations,

  • 4x - 3y - 18 = 0
  • 4y - 5x - 7 = 0

⇒ 4x - 3y - 18 = 0

    4x - 3y = 18  ---[1]

⇒ 4y - 5x - 7 = 0

   -5x + 4y = 7  ---[2]

Multiply equation [1] by 4,

 4(4x - 3y) = 4(18)

  16x - 12Y = 72  ---[3]

Multiply equation [2] by 3,

 3(-5x + 4y) = 3(7)

 -15x + 12y = 21  ---[4]

Add equations [3] and [4],

  16x - 12y + (-15x + 12y) = 72 + 21

  16x - 12y - 15x + 12y = 93

          x = 93

Substitute x = 93 in equation [1],

  4x - 3y = 18

  4(93) - 3y = 18

    372 - 3y = 18

     3y = 372 - 18

     3y = 354

       y = 354/3

      y = 118

Therefore, x = 93 and y = 118

Verification :

  • x = 93
  • y = 118

[1] : 4x - 3y = 18

       4(93) - 3(118) = 18

      372 - 354 = 18

        18 = 18

       LHS = RHS

[2] : 4y - 5x = 7

     4(118) - 5(93) = 7

      472 - 465 = 7

          7 = 7

         LHS = RHS

Hence verified!


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