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

1. ## 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.

2. ## Re: Solution needed to equation - think it is termed a linear equation???

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 $y=-2x+50$

3. ## 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?

4. ## Re: Solution needed to equation - think it is termed a linear equation???

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;

5. ## Re: Solution needed to equation - think it is termed a linear equation???

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
...