Question

The solution of the equation ax + by + 5 = 0 and bx – ay – 12 = 0 is (2, – 3). Find the values of a and b.

Answer 1

Since (2, – 3) is the solution of ax + by + 5 = 0 and bx – ay – 12 = 0, the point (x, y) = (2, – 3) satisfies the given equations.

ax + by + 5 = 0

∴ ax + by = –5    ...(i)

bx – ay – 12 = 0

∴ bx – ay = 12   ...(ii)

Putting x = 2 and y = – 3 in equations (i) and (ii), we get

2a – 3b = –5   ...(iii)

2b + 3a = 12

i.e., 3a + 2b = 12   ...(iv)

Multiplying equation (iii) by 2, we get

4a – 6b = –10   ...(v)

Multiplying equation (iv) by 3, we get

9a + 6b = 36   ...(vi)

Adding equations (v) and (vi), we get

    4a – 6b = –10
+ 9a + 6b = 36   
   13a        = 26

∴ a = `26/13`

∴ a = 2

Substituting a = 2 in equation (iv), we get

3(2) + 2b = 12

∴ 6 + 2b = 12

∴ 2b = 6

∴ b = `6/2`

∴ b = 3

∴ a = 2 and b = 3