## 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.​

Question

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.​

in progress 0
1 month 2021-08-16T06:56:35+00:00 1 Answers 0 views 0

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 ?

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 .