Solve

Asked by  | 22nd Jul, 2010, 03:53: PM

Expert Answer:

Dear Student,

 
We can solve this pair of linear equations using elimination method
 
The given equations are:
 
ax + by = a - b ...................(i)
 
bx - ay = a + b ...................(ii)
 
 
multiplying (i) with b and (ii) with a, we get
 
bax + b2y = b(a - b)      ............(iii)
 
and
 
abx - a2y = a(a + b)     ..............(iv)
 
 
Now, we subtract (iv) from (iii) so that x is eliminated
 
We get
 
b2y + a2y = b(a - b) - a(a + b)
 
(b2 + a2)y = ba - b2 - a2 - ab
 
(b2 + a2)y =  - b2 - a2
                =  - (b2 + a2)
 
So we get y = - (b2 + a2)/(b2 + a2) = -1
 
Substituting this value of y in (i), we get
 
ax + b(-1) = a - b
 
ax - b = a - b
 
i.e.    ax = a
 
which means x = 1
 
Hence the solution is x = 1, y = -1
 
 
 
Regards,
 
Team Topper Learning
 
 
 
 
 
 
 

Answered by  | 22nd Jul, 2010, 06:41: PM

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