SOLUTION: [(1+b)/b](x) + [(1+a)/a](y) = b-a x/a - 4y/b = 5 Need help please. I got this problem in a linear equation worksheet. But as the equation has a degree of more than one, i'm po

Algebra ->  Systems-of-equations -> SOLUTION: [(1+b)/b](x) + [(1+a)/a](y) = b-a x/a - 4y/b = 5 Need help please. I got this problem in a linear equation worksheet. But as the equation has a degree of more than one, i'm po      Log On


   

Question 755197: [(1+b)/b](x) + [(1+a)/a](y) = b-a
x/a - 4y/b = 5
Need help please. I got this problem in a linear equation worksheet. But as the equation has a degree of more than one, i'm posting this here. Please help as soon as possible.
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
Those equations have x and y to degree 1. Each equation can be simplified but the degrees on x and y will still be 1.

[(1+b)/b](x) + [(1+a)/a](y) = b-a
As rendered should be as
%28%281%2Bb%29%2Fb%29%28x%29+%2B+%28%281%2Ba%29%2Fa%29%28y%29+=+b-a
Multiply both sides by a%2Ab to clear the fractions.

x%2Fa+-+4y%2Fb+=+5
See the l.c.d. is also a%2Ab, so multiply both sides by a%2Ab to clear the fractions.

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I'll jump ahead some, since you may already know how to clear the fractions and simplify each of these simultaneous equations. You will find you have this system linear in x and y, exponent on x and y being 1:

-------------------------------
a%281%2Bb%29x%2Bb%281%2Ba%29y=ab%5E2-ba%5E2
AND
bx-4ay=5ab
-------------------------------

I would recommend solving the second equation for either x or y and subsitute into the first equation and solve for the single variable there; and then solve for the other variable. I'll give one of those pathways here:

bx-4ay%2B4ay=5ab%2B4ay
bx=5ab%2B4ay
x=%285ab%2B4ay%29%2Fb
and substitute this for x in the other equation.

a%281%2Bb%29x%2Bb%281%2Ba%29y=ab%5E2-ba%5E2
a%281%2Bb%29%281%2Fb%29%285ab%2B4ay%29%2Bb%281%2Ba%29y=ab%5E2-ba%5E2
.
Many very detailed simplification steps too difficult to show in typed text form, so done on paper, yielding this not necessarily finished solution for only y:
.
.
y=b%28ab%5E2-ba%5E2-5a%5E2%281%2Ba%29%29%2F%284a%5E2%281%2Bb%29%2Bb%5E2%281%2Ba%29%29
Seems to have no special useful factorizations there so the best simplification is


Best way to find x is to go back to the second equation and solve that for y and substitute into the first equation and go through the long steps to solve for a formula for x.