Question

Solve the following two linear equation by substitution and elimination method: `ax+by=(a-b) , bx-ay=(a+b)` ?

Answer 1

Solution is `x=1` and `y=-1`

Explanation:

Here we find the value of one variable (say `y`), from one equation, in terms of other variable, and then put its value in other to eliminate and find the value of other variable. Then, we can put value of this variable in any of the two equations and get the value of other variable.

As `ax+by=a-b`, `by=a-b-ax` and `y=(a-b-ax)/b`

putting this in second equation eliminates `y` and we get

`bx-a(a-b-ax)/b=a+b` and multiplying by `b` we get

`b^2x-a^2+ab+a^2x=ab+b^2`

or `x(a^2+b^2)=a^2+b^2`

and hence `x=1`

Putting this in first equation `a+by=a-b`

or `by=-b` i.e. `y=-1`

Hence solution is `x=1` and `y=-1`