9) The solution of the equation a x + b y + 5 = 0 and b x – a y – 12 = 0 is
(2, -3)
Find the values of a and b.​

1 thought on “9) The solution of the equation a x + b y + 5 = 0 and b x – a y – 12 = 0 is<br />(2, -3)<br />Find the values of a and b.​”

1. Given :– The solution of the equation ax + by + 5 = 0 and bx – ay – 12 = 0 is (2, -3) .

   To Find :–

   • The values of a and b ?

   Answer :–

   putting values of x and y we get,

   → ax + by + 5 = 0

   → a * 2 + b * (-3) + 5 = 0

   → 2a – 3b + 5 = 0

   → 2a – 3b = (-5) ———– Eqn.(1)

   and,

   → bx – ay – 12 = 0

   → b * 2 – a * (-3) – 12 = 0

   → 2b + 3a – 12 = 0

   → 3a + 2b = 12 ———– Eqn.(2)

   multiply Eqn.(1) by 3 and Eqn.(2) by 2 and then subtracting the result we get,

   → 3(2a – 3b) – 2(3a + 2b) = 3(-5) – 2*12

   → 6a – 6a – 9b – 4b = – 15 – 24

   → – 13b = – 39

   → b = 3 (Ans.)

   putting value of b in Eqn.(2) ,

   → 3a + 2 * 3 = 12

   → 3a + 6 = 12

   → 3a = 12 – 6

   → 3a = 6

   → a = 2 (Ans.)

   Hence, value of a and b are 2 and 3 respectively .

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