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

Given: ax + by = 7 …(i)

bx + ay = 5 …(ii)

intersection point of equation (i) and (ii) is (3,1) which means point (3,1) lies on both the lines which concludes us that point (3,1) will satisfy both the equations

Therefore

3a + b = 7 …(iii)

3b + a = 5 ⇒ a = 5 – 3b …(iv)

Putting a = 5 – 3b in equation (iii)

⇒ 3 × (5 – 3b) + b = 7

⇒ 15 – 9b + b = 7

⇒ 15 – 8b = 7

⇒ 8b = 15 – 7

⇒ 8b = 8

∴ b = 1

Put b = 1 in equation (iv)

⇒ a = 5 – (3 × 1)

⇒ a = 5 – 3

∴ a = 2

Therefore a = 2 and b = 1