Question

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

Answer 1

given equations are :
ax + by = 7..........(1)
bx + ay = 5 .........(2)

according to question, (3,1) is the point of intersection of given equations.
so, (3,1) will satisfy both of given equations.

put (3,1) in equation (1),
3a + b = 7 ........(3)

put (3,1) in equation (2),
3b + a = 5......... (4)


multiplying 3 with equation (3) and then subtracting equation (4),

3(3a + b) - (3b + a) = 3 × 7 - 5

9a + 3b - 3b - a = 21 - 5

8a = 16 => a = 2 , put it in equation (3)

b = 7 - 3a = 7 - 6 = 1

hence, a = 2 and b = 1

Answer 2

Answer:

a=2 and b=1

Step-by-step explanation:

Concept:

The point of intersection of two lines is obtained by solving their respective equations.

The point of intersection is the only common point to both the lines.

Given lines are

ax+by - 7 = 0

bx+ay - 5 = 0

since the point of intersection of the given lines is (3,1),

we have,

3a+b-7=0.......(1)

3b+a-5=0

a+3b-5=0......(2)

By cross multiplication rule, we get

$\frac{a}{-5+21}=\frac{b}{-7+15}=\frac{1}{9-1}\\\\\frac{a}{16}=\frac{b}{8}=\frac{1}{8}\\\\a=\frac{16}{8}=2\\\\b=\frac{8}{8}=1$

Therefore

a=2 and b=1

I hope this answer helps you