Question

the coordinates of point of intersection of line X + B Y is equal to 9 and b x + Y is equal to 5 is 3 and minus 1 find the value of a and b
solution:

ax
$ax + by = 9$
$bx + ay = 5$
D


is equal to a square minus b square
Dx is equal to 9a minus 5 b
D Y is equal to 5a - 9b
x is equal to DX upon D and Y is equal to DY upon D
according to data
3 is equal to 9a - 5b upon a square minus b square and minus 1 is equal to 5 a minus 9 b upon a square minus b square
therefore 3(a square minus b square )is equal to 9a - 5b equation 1
a square minus b square is equal to 9a - 5 b equation 2
from equations 1 and 2
3(9a-5b)is equal to 9a-5b
therefore
27a-15b is eqaul to 9a-5b
therefore
32 b is equal to 24 a
therefore
4 b is equal to 3 a
therefore a upon b is equal to 4 Upon 3
therefore
a is equal to 4 and b is equal to 3 is it correct solution ​

Answer 1

a simple solution to this question would be......

we know that,

ax+by=9

bx+ay=5

now if the coordinates of point of intersection of the 2 lines is (3,-1).

then it is clear that (3,-1) lies on both the lines.

now place the values of x and y in both the equations.

it becomes....

3a-b=9 .......eq 1

3b-a=5 .......eq 2

now multiply eq 2 by 3,

3(-a+3b=5)

-3a+9b=15 ........eq 3

now add eqs 1 & 3,

3a-b-3a+9b =9+15

8b=24

b=3

now put value of 'b' in eq 1,

3a-3=9

3a= 9+3

3a=12

a=4

hence, a=4, b=3.

hope it helps you......