solving equations by the method of elimination a x + b y = a 2 + b 3 … ( i ) x + 1 = y … ( i i )We have to solve for x and y, only this time using the method of elimination.From equation ( i i ), we get, 1 x + 1 = 1 y ⇒ b x + 1 = b y … ( i i i )Subtracting ( i i i ) from ( i ), we get, a x + b y − b y = a 2 + b 3 − b x + 1 ⇒ a x = a 2 + b 3 − b x + 1 After that,I really cannot find anything to do.I have taken quite a few other routes, but have hit nothing but dead ends. At this a point a little hint will be appreciated.

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solving equations by the method of elimination      a    x    +      b    y    =      a    2    +      b    3          …  (  i  )  x  +  1  =  y        …  (  i  i  )We have to solve for x and y, only this time using the method of elimination.From equation   (  i  i  ), we get,      1          x      +      1        =      1    y    ⇒      b          x      +      1        =      b    y          …  (  i  i  i  )Subtracting   (  i  i  i  ) from   (  i  ), we get,      a    x    +      b    y    −      b    y    =      a    2    +      b    3    −      b          x      +      1        ⇒      a    x    =      a    2    +      b    3    −      b          x      +      1      After that,I really cannot find anything to do.I have taken quite a few other routes, but have hit nothing but dead ends. At this a point a little hint will be appreciated.

Miriam Payne · Accepted Answer

You&#039;ve already done the &quot;elimination&quot; when you subtract (iii) from (i), and it looks like you have a typo, y should be completely eliminated when you do the subtraction, and you should get  a  /  x  =  a  /  2  +  b  /  3  −  b  /  (  x  +  1  )If you then multiply this equation by   x  (  x  +  1  ) on both sides (keeping in mind then that   x cannot be   0 or   −  1), and cancel the   x and   (  x  +  1  ) in denominators, and then expand and bring all terms to one side then you will get a quadratic in   x that is set to 0, which you can solve for   x. Then you can substitute into (ii) to easily get   y.Note that when you solve the quadratic, you are assuming either   a  ≠  0 or   b  ≠  0. If   a  =  b  =  0 then any   x gives a solution except   x  =  0 and   x  =  −  1.

Alaina Marshall · Accepted Answer

Great expert answer!

solving equations by the method of elimination a x </mfrac> + b

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