Question 133632
This problem deals with the addition method, and I need help. 

2a + 3b = -1
3a + 5b = -2

You have two equations in two variables.  The variables are a and b.

What you are looking for is a point in the (a,b) form that indicates where the two equations meet on the coordinate plane.  The point where the two equations meet is the solution of this system of equations.  In order to know the a and b values, you were told to use the addition method.  In this method, you must use a number (it could be fraction) to multiply either questions by for the sole purpose of doing away with either a or b as step one.  The fun thing here is the fact that YOU choose which letter you want to delete first.

I want to remove letter a first.

To do this, I need to multiply EITHER equation by a number (or fraction) that will CANCEL OUT a in BOTH given equations.

Which number? Which fraction?

I will call 2a + 3b = -1 Equation A and
3a + 5b = -2 Equation B for you to follow my notes easier.

2a + 3b = -1...Equation A
3a + 5b = -2...Equation B

I will multiply Equation B by -2/3.  Using -2/3 will create a -2a in Equation B, which will then allow me to do away with the a letter in both equations.

Are you with me so far?

-2/3 times 3a = -2a

-2/3 times 5b = -10b/3

-2/3 times -2 = 4/3

We now have this:

2a + 3b = -1...Equation A
-2a -10b/3 = 4/3...This is our new Equation B.

Do you see that NOW I can delete or do away with 2a and -2a.  These two terms cancel out because one is positive and the other is negative.

We now add the rest of the terms in Equations A and B.

+3b - 10b/3 = -b/3

-1 + 4/3 = 1/3

We now have this equation:

-b/3 = 1/3

To remove the fractions, simply multiply BOTH sides of the equation by the denominator 3.

Doing so, we get this:

-b = 1

Now, divide BOTH sides by -1 to find the value of b.

b = 1/-1

b = -1

We just found the value of b.

Here comes the easy part.

Plug the value of b I just found into EITHER Equation A or B to find the value of a. 

I will use Equation A.

Let b = -1

2a + 3(-1) = -1

2a - 3 = -1

2a = -1 + 3

2a = 2

a = 2/2

a = 1

The solution for your equations is: a = 1 and b = -1.

Did you follow?

NOTE:  What does a = 1 and b = -1 really mean?  It means that BOTH equations given to you will meet or touch each other when graphed on the coordinate plane at the point (1, -1).  Is this clear?