Question

the coordinates of the points of intersection of lines ax+by=9 and bx+ay=5 is (3,minus 1). find the values of a and b​

Answer 1

Answer:

hence, a = 4 and b = 3

Step-by-step explanation:

given equations are :

ax + by = 9..........(1)

bx + ay = 5 .........(2)

as given, (3, -1) is the point of intersection in equation.

so, (3,-1) will satisfy both of given equations.

put (3,-1) in equation (1),

3a - b = 9 ........(3)

put (3,-1) in equation (2),

3b - a = 5......... (4)

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

3(3a - b)+ (3b - a) = 3 × 9 + 5

9a - 3b + 3b - a = 27 + 5

8a = 32

a = 4 , put it in equation (3)

3(4) - b = 9

12-b=9

-b=9-12

b=3

hence, a = 4 and b = 3

Answer 2

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

ax+by=9

bx + ay = 5

as both lines intersect on point (3,-1)

so this point lies on both line hence

satisfies the line equation

3a - b = 9

3b - a = 5

adding both

2a +2b =14

a + b = 7

b = 7-a

3a -(7-a) = 9

4a - 7 = 9

4a = 16

a = 4

b = 7-4 = 3

a = 4

b = 3