8
2 3
x y
or 8
6
3 2
x y
or 3 x 2 y 48 0
Again, 3 3
4
5
y
x
or 3
4
5 12
x y
or 5 x 12 y 12 0
? the given equations are : 3 x 2 y 48 0
5 x 12 y 12 0
By the method of cross-multiplication, we get,
3 12 5 2
1
2 12 12 48 48 5 12 3 u u
u u
u ( )u( ) ( ) ( )
x y
x y 1
5 12 12 5 12
3 2 48 3 2
or
36 10
1
24 576 240 36
x y
or
46
1
552 276
x y
or
46
1
552 276
x y
?
46
1
552
x
or, 12
46
552
x
Again,
46
1
276
y
, or 6
46
276
y
? Solution (x,y) ( 12 , 6 )
Verification of the correctness of the solution :
Putting the values of xandy in given equations, we get,
In 1st equation, L.H.S. = 6 2
3
6
2
12
2 3
x y
8 R.H.S.
In 2nd equation, L.H.S. = 3 6
4
5 12
3
4
5
u
u
y
x
15 18 3 = R.H.S.
? the solution is correct.
Example 6. Solve by the method of cross-multiplication : axby ab bxay.
Solution : Given equations are
¿
¾
½
bx ay ab
ax by ab
or,
¿
¾
½
0
0
bx ay ab
ax by ab
By the method of cross-multiplication, we get,