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.

Many thanks in advance.

Darren.

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: $\displaystyle \left\{\left(x,-2x+50.\right)\right\}$.

Pick any value for $\displaystyle x$ and then you have a value for $\displaystyle y=-2x+50$

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?

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.

Many thanks in advance.

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;

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

...