Use the linear combination method to solve the system of equations. explain each step of your solution.

-4x + 9y = 9
x - 3y = -6

(9,5)

Step-by-step explanation:

Linear combination (also known as elimination) is trying to somehow combine the equations together so that it eliminates one variable in order to solve for the other one.

So you have

-4x+9y=9

  x-3y =-6

In elimination, you want the equations to be in the same form which they are here in this case.  You want one of the columns to contain opposites or sames.

If opposites, you add the equations.

If sames, you subtract the equations.

We have neither opposites or sames in either of the first two variable columns which is where we want one of these columns to be.

So I'm going to multiply the bottom equation by 3.  This is not the only way. This is the way I'm going to do it. You could decide to multiply the bottom equation by 4 or -4 or -3 instead.  

So anyways multiply bottom equation by 3. This is what my system looks like now:

 -4x+9y=9

  3x-9y=-18

  Now we get to add this equations because the 2nd column,

                     the y column, we have opposites.

adding now

 -1x+0y=-9                  -4+3=1 and -9+9=0  and 9+-18=0      

  -x      =-9                    -1x=-1*x=-x     and 0y=0*y=0

   x      =9                       Take opposite of both sides

Now once we find one variable we must obtain the other variable by replacing x with 9 and solving for y in one of the equations (don't use both-just choose one- doesn't matter which)

x-3y=-6 was the second equation before manipulation

Plug in 9 for x

9-3y=-6

Subtract 9 on both sides

 -3y=-6-9

  -3y=-15  

Divide both sides by -3

    y=5

So the solution is (x,y)=(9,5)

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