Question

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

Answer 1

`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)`