Question

If the point of intersection of ax + by = 7 and bx + ay = 5 is (3,1), then find the value of a and b.

Answer 1

ax + by = 7 and bx + ay = 5

The point of intersection lies on both the equations

It will satisfy the given equation

ax + by = 7

put x = 3 and y = 1

3a + b = 7  ................. (1)

bx + ay = 5 [Given]

put x = 3 and y = 1

`therefore` 3b + a = 5 .................. (2) 

Adding equation (1) and (2)

   3a + b = 7
   a + 3b = 5
____________________
  4a + 4b = 12

`therefore` 4 (a - b) = 12

`therefore a + b = 12/4`

a + b = 3 ....(3)

Suntracting equation (1) and (2) 

  3a + b = 7
   a + 3b = 5 
________________
  2a - 2b = 2

2 (a - b) = 2

a - b = `2/2`

a - b = 1 ....(4)

Adding equation (3) and (4) 

   a + b = 3
   a - b = 1
____________
     2a = 4

 a = `4/2`

 a = 2

Substituting a = 2 in equation (3)

3a + b = 7

3(2) + b = 7

6 + b = 7

b = 7 - 6

b = 1