Question

the coordinates of the points of intersection of lin ax+by=9 and bx+ay=5 is (3,-1).find the value of a and b.

Answer 1

Answer:

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

the coordinates of the points of intersection of lin ax+by=9 and bx+ay=5 is (3,-1).find the value of a and b.

ax + by = 9

bx + ay = 5

adding both

3,-1 is intersection point so it lies on both line and will satisfy both line equations

3a - b = 9 eq1

3b - a = 5 eq2

3*eq1 + eq2

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

8a = 27 + 5

8a = 32

a = 4

3b -4 =5

3b = 9

b = 3

a =4 & b = 3