- In example #3 in this section, it seems that Mr Foerster is using the linear combination system to solve the problem algebraically. But then instead of adding the two equations as he taught us on p. 314, he subtracts them!

Why?

--shannon - Subtraction is actually addition of the negative. 5 minus 2 is defined as 5 + (-2). Similarly, for division, 8 divided by 2 is defined as 8 times 1/2. Algebraically speaking, there are two primary operations: addition and multiplication. The other two operations are defined as operating on the inverse.

Personally, when I do the linear combination method and a subtraction is required I take two steps: I multiply one equation through by -1 then I add. This avoids sign errors. I teach it this way, I believe, in my video lessons.

--David ChandlerOn Wed, Oct 3, 2012 at 9:55 AM, shannon Stoney <shannonstoney@...> wrote:

In example #3 in this section, it seems that Mr Foerster is using the linear combination system to solve the problem algebraically. But then instead of adding the two equations as he taught us on p. 314, he subtracts them!

Why?

--shannon

- I was thinking about this later and realized that if you read the explanation of why linear combination works in Foerster's text, he explains that it works because you can add equal quantities to both sides of an equation. So, by the same token, you can subtract equal quantities from both sides, I guess. So there's no reason why you can't combine two equations by subtracting as well as adding.In some of his examples he multiplies one equation by -1 before adding, but in that example in 10-8, he just subtracted without really going into the reasons. I can go into the reasons, though, when I explain it tomorrow!Thanks,--shannonOn Oct 3, 2012, at 1:14 PM, David Chandler wrote:
Subtraction is actually addition of the negative. 5 minus 2 is defined as 5 + (-2). Similarly, for division, 8 divided by 2 is defined as 8 times 1/2. Algebraically speaking, there are two primary operations: addition and multiplication. The other two operations are defined as operating on the inverse.

Personally, when I do the linear combination method and a subtraction is required I take two steps: I multiply one equation through by -1 then I add. This avoids sign errors. I teach it this way, I believe, in my video lessons.

--David ChandlerOn Wed, Oct 3, 2012 at 9:55 AM, shannon Stoney <shannonstoney@...> wrote:

In example #3 in this section, it seems that Mr Foerster is using the linear combination system to solve the problem algebraically. But then instead of adding the two equations as he taught us on p. 314, he subtracts them!

Why?

--shannon