How to solve each of the following pairs of simultaneous equations for x and y? 1) #ax + y = c and x+by=d#

1 Answer
Jan 23, 2018

#x=(d-bc)/(1-ab)# and #y=(c-ad)/(1-ab)#

Explanation:

The best way is to use substitution method. We get #y# from first equation and put its value from it in second equation to get #x#.,

As #ax+y=c#, we have #y=c-ax#

putting this value in second equation we get

#x+b(c-ax)=d#

or #x+bc-abx=d#

or #x(1-ab)=d-bc#

i.e. #x=(d-bc)/(1-ab)#

Hence #y=c-axx(d-bc)/(1-ab)#

= #((c-abc-ad+abc))/(1-ab)#

i.e. #y=(c-ad)/(1-ab)#