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**[SOLVED] Inverse signs on both sides of an equation [Confusion]**

Hey everyone,

I've just reinserted myself in maths after so many years, done a lot of review but I sometimes fall on small "glitches" between my test answers and the suggested answers in my textbook.

I've been getting confused with a new "trick":

Right now I'm at getting solution-pairs to solve systems of equations, graph them after getting

*y = mx + b*, etc (sorry if my terminology is still shaky) and on previous pages (in the textbook) I noticed that you could cancel out like a -y and make it y (positive) by inverting all signs on the other side of the equation.

Everything seemed to work okay and I was all hyped about this new trick until I found the detailed answer (step by step) to be different and break that rule I thought I had learned. I'll copy the last two steps from what the answer section gives me :

Fig. 1

\(\displaystyle y = \frac{-2x}{-3} - \frac{14}{-3}\)

*then becomes:*

\(\displaystyle y = \frac{2x}{3} + \frac{14}{3}\)

**My confusion :**

Why does the right side of the equation invert all signs when the left one did not (stayed positive Y). Of course, that's what we want at the end, a positive y, but I don't understand why it remains positive while the rest all inverts (if "invert" is the correct term).

Here's an example among others that led me to believe BOTH SIDES would be affected when inverting (afterall, it's an

*equation*)

Example 1:

\(\displaystyle -y = -2x - 5\)

*becomes...*

\(\displaystyle y = 2x + 5\)

Here, you invert -y to +(1)y for convenience and subsequently invert all signs on the other side of the equation. My problem lies in the fact Fig 1 (first equation) has y remain positive y but yet all signs change on the other side.

I'd hugely appreciate any explanation and/or hints.

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