5q+3t = 7, 2q-3t= 7 (Minor help with manipulation)

Question

Here's the solution. I need help if someone can explain this to me.

When the problem is manipulated at the beginning, this is what happens.

2q – 3t = 7 
-3t = -2q + 7 (I'm not following this part) Can someone explain why the negatives stay) 
3t = 2q – 7 (And why the negatives come off after) (This is the way my brain thinks the problem is from the first place)

I'm not sure why the negative signs are used in the second step? Can someone explain. 
There's no need to solve the rest, this is the part that is messing me up.

roygush · Answer

ok, lets see if this makes sense. if you have this: 2q – 3t = 7 and you want to isolate either "t" or "q" what you did is the same as: 1) 2q – 3t = 7 2) 2q - 2q - 3t = 7 -2q we moved from step a to step b by adding -2q to both sides of the equation. in this way we will get -3t = 7 - 2q. all the manipulations you do on one side of the equation should also be on the other side in order to keep both sides satisfied. if im not clear enough ill try again. edit: for the last part of your question: 3) 3t = 2q - 7. we just multiplied both sides by -1. it was originally - -3t = 7 - 2q / (multiply -1) and we get 3t = 2q - 7. notice that if the equation has < or > and you multiply by -1, you need to switch the sign. if it was < , no it should be > and vise versa.

feellikequitting · Answer

But this still leaves -3T=7-2Q

How does that become positive?

roygush · Answer

i just edit my answer, read the last part.

you need to multiply both sides of the equation by -1. you dont have to do it, its just better when the variables are positive and not negative.

arnivorous · Answer

(1) 2q – 3t = 7 
(2) -3t = -2q + 7 (I'm not following this part) Can someone explain why the negatives stay) 
(3) 3t = 2q – 7 (And why the negatives come off after) (This is the way my brain thinks the problem is from the first place)

Equation (1)->(2). Subtracted 2q from both sides.
Equation (2)->(3). Multiplied both sides by -1.

GMATPill · Answer

The last step is just switching the signs (OR multiplying by -1).

The goal usually is to isolate a variable on one site and at least have it be positive. In this case, 3t.

Then when you're ready to solve for t, you just decide both sides by 3 to get t= some expression.

5q+3t = 7, 2q-3t= 7 (Minor help with manipulation)

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