How do I solve a system of equations with multiple unknowns?

[ProBasket]

original question: \int (x^2+2x-1)/(x(2x-1)(x+2))

the following is from my math book:
2A + B + 2C = 1
3A + 2B - C = 2
-2A = -1

okay i understand everything the math has done up to this point, this is the point that i don't get:

A = 1/2, B = 1/5, C = -1/10

i think the book got A from solving this equation: -2A = -1

I just want to know how the book got A, B, and C.

 

[gnome]

If those are the values for A, B and C given in the book, apparently -2A=1 was supposed to be 2A=1. Otherwise all those values are wrong.

(But what does that have to do with partial fractions?)

 

[ProBasket]

If those are the values for A, B and C given in the book, apparently -2A=1 was supposed to be 2A=1. Otherwise all those values are wrong.

(But what does that have to do with partial fractions?)

my bad, it was a typo. it's suppose to be -2A = -1

and it has to do with partial fractions because it's a partial fractions question.

 

[Hurkyl]

Sure, the question came from a partial fraction problem... but partial fractions have nothing to do with its solution.

The problem is now purely algebraic: you have a system of equations with several unknowns. Do you remember anything from your algebra classes about solving them?

 

[ProBasket]

Sure, the question came from a partial fraction problem... but partial fractions have nothing to do with its solution.

The problem is now purely algebraic: you have a system of equations with several unknowns. Do you remember anything from your algebra classes about solving them?

nevermind, i got it. wow i can't believe i didnt get it. i was thinking too hard