Solve the following pair of linear equations by the method of cross-multiplication. axby=a+bbx+ay=ba


Answer:

x=1  and  y=1

Step by Step Explanation:
  1. The given pair of equations is axby=a+b   axby(a+b)=0bx+ay=ba   bx+ay(ba)=0
  2. By cross-multiplication, we get xba(a+b)(ba)=yab(a+b)(ba)=1abbaxb×(ba)a×(a+b)=y(ba)×a+(a+b)×b=1a×ab×(b)xb(ba)+a(a+b)=ya(ba)+b(a+b)=1(a2+b2)xb2ba+a2+ab=yab+a2+ba+b2=1(a2+b2)x(b2+a2)=y(b2+a2)=1(a2+b2)x(b2+a2)=1(a2+b2)  and  y(b2+a2)=1(a2+b2)x=(b2+a2)(a2+b2)  and  y=(b2+a2)(a2+b2)x=1  and  y=1
  3. Hence, the required solution is x=1 and y=1.

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