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How to Solve the system of equations using the Addition method?

Solve the system of equations using the Addition method.

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

I thought you had to be able to eliminate a variable in the first step meaning the +5b would have to be -3b, otherwise i have no clue how to do this, can anyone help me? If you give an answer please explain.

You can MAKE a variable cancel by multiplying each equation by the coefficient of the variable you want to eliminate. For example:

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

Say we wnat to eliminate the "a" term. The first equation has "2a" and the second one has "3a." Multiply the first equation by 3 and the second equation by 2.

6a + 9b = -3
6a + 10b = -4

Now subtract the second equation from the first one.

. .6a + 9b = -3
- .6a + 10b = -4
==============
-b = 1 . . . . .so b = -1; to find a, put b = -1 into either of the two original equations.

Using eq. 1, 2a + 3(-1) = -1
2a - 3 = -1
2a = 2
a = 1

This entry was posted on Tuesday, January 5th, 2010 at 11:41 pm and is filed under addition. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.

4 Responses to “How to Solve the system of equations using the Addition method?”

  1. BF Says:
    January 6th, 2010 at 5:22 am

    multiply the first equation by -3/2 (both sides) to give you -3a -9/2b=3/2
    Add the two equations together. The a’s will cancel out and you will be left with only b. Solve for b. Once you have solved for b, plug that value into either of the equations to get a.
    References :

  2. Ghr Says:
    January 6th, 2010 at 5:40 am

    equation number 1 time 3 and the second equation time -2
    we get
    6a+9b=-3
    -6a-10b=4

    the we add them together
    -b=1
    b=-1
    we replace in 1 :2a-3=-1 give us a=1
    References :

  3. HPV Says:
    January 6th, 2010 at 5:55 am

    You can MAKE a variable cancel by multiplying each equation by the coefficient of the variable you want to eliminate. For example:

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

    Say we wnat to eliminate the "a" term. The first equation has "2a" and the second one has "3a." Multiply the first equation by 3 and the second equation by 2.

    6a + 9b = -3
    6a + 10b = -4

    Now subtract the second equation from the first one.

    . .6a + 9b = -3
    - .6a + 10b = -4
    ==============
    -b = 1 . . . . .so b = -1; to find a, put b = -1 into either of the two original equations.

    Using eq. 1, 2a + 3(-1) = -1
    2a - 3 = -1
    2a = 2
    a = 1
    References :

  4. Filby Says:
    January 6th, 2010 at 6:28 am

    Remember that you can add as well as subtract equations ad you can multiply equations by anything as long as you do the same to both sides

    2a + 3b = -1
    multiply b 3
    6a + 9b = -3

    3a + 5b = -2
    multiply by 2
    6a + 10b = -4

    You now have 6a in both
    Subract the second from the first
    (6 - 6)a + (10- 9)b = (-4 - (-3))
    b = -1
    so a = +1
    References :

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