# Solution needed to equation - think it is termed a linear equation???

• Mar 13th 2012, 03:52 PM
iksotof
Solution needed to equation - think it is termed a linear equation???
Hi

Excuses first, it is over 20 years since school and I have had no cause to do equations since. I realise this may be rudimentary, no less what is the solution please to:

4000=(80 * Y) + (160 * x)

An explanation would ne nice too.

Darren.
• Mar 13th 2012, 04:08 PM
Plato
Re: Solution needed to equation - think it is termed a linear equation???
Quote:

Originally Posted by iksotof
I realise this may be rudimentary, no less what is the solution please to:
4000=(80 * Y) + (160 * x)

There is really no single solution in the sense that I think you mean solution.
There is a set of solutions, a set of ordered pairs: $\left\{\left(x,-2x+50.\right)\right\}$.
Pick any value for $x$ and then you have a value for $y=-2x+50$
• Mar 13th 2012, 04:18 PM
iksotof
Re: Solution needed to equation - think it is termed a linear equation???
Thanks for this, I was just after the value of x an y?
• Mar 13th 2012, 11:15 PM
princeps
Re: Solution needed to equation - think it is termed a linear equation???
Quote:

Originally Posted by iksotof
Hi

Excuses first, it is over 20 years since school and I have had no cause to do equations since. I realise this may be rudimentary, no less what is the solution please to:

4000=(80 * Y) + (160 * x)

An explanation would ne nice too.

Darren.

You can use this Maple code to find nonegative integer solutions :

Code:

for x from 0 to 50 do for y from 0 to 50 do if 50=2*x+y then print(x,y); end if; end do; end do;
• Mar 14th 2012, 08:21 AM
Wilmer
Re: Solution needed to equation - think it is termed a linear equation???
Quote:

Originally Posted by iksotof
4000=(80 * Y) + (160 * x)

Divide by 80: 50 = y + 2x

An integer solution exists for ALL values of x:
Code:

 x  2x  y  2x+y  1    2  48    50  2    4  46    50  3    6  44    50 ... 24  48  2    50 25  50  0    50 26  52  -2    50 27  54  -4    50 ...