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

1 Answer
Jan 23, 2018

x=(d-bc)/(1-ab)x=dbc1ab and y=(c-ad)/(1-ab)y=cad1ab

Explanation:

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

As ax+y=cax+y=c, we have y=c-axy=cax

putting this value in second equation we get

x+b(c-ax)=dx+b(cax)=d

or x+bc-abx=dx+bcabx=d

or x(1-ab)=d-bcx(1ab)=dbc

i.e. x=(d-bc)/(1-ab)x=dbc1ab

Hence y=c-axx(d-bc)/(1-ab)y=ca×dbc1ab

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

i.e. y=(c-ad)/(1-ab)y=cad1ab