Solve the system by the addition method.

Question

-4x - 2y = -20
-9x - 6y = -36

Answer 1

These equations are rather interesting:

  -4x - 2y = -20     is the same as    -2x - y = -10  is the same as    2x + y = 10
and

  -9x - 6y = -36   is the same as   -3x - 2y = -12  is the same as    3x + 2y = 12

 

The elimination (addition/subtraction) method gets the coefficient of one variable to be the same or opposite, then eliminates that variable by addition/subtraction.

 

With these equations, you have multiple possibilities.  Let's use:

-4x - 2y = -20       (original first equation)

 3x + 2y = 12         (modified second equation)

------------------    (elimination; add equations)

 -x         = -8

  x         = 8               (eq3)

 

  2x         = 16             (multiply eq3 by 2)

 -2x - y   = -10      (modified first equation)

-----------------     (elimination; add equations)

       -y    =  6

        y    = -6

Answer 2

To solve a system using the addition method, we use both equations simultaneously to eradicate one variable, solve for the other variable that we kept, and then plug the variable that we found into one equation to solve for the variable that we initially eradicated.

 

You can solve for either x or y. I choose to solve for x, which means that I need to get the y terms to cancel out.

To do that, I multiply the first equation by -3 so that I will get the y-term to equal 6y. I end up with the following:

 

-3(-4x - 2y = -20)

I now distribute the -3. **Remember that you must multiply the ENTIRE equation by the -3 (and in other cases, by whatever factor you need to get one term to cancel out with another!)

 

12x + 6y = 60

 

Now I recommend lining up the two equations with one beneath the other as follows:

12x + 6y = 60

-9x - 6y = -36

The 6y and -6y cancel out since I am adding the two equations together.

I am left with the following:

3x = 24

x = 8

 

Now I use x = 8 and plug it into either of the two ORIGINAL equations. I will plug it into the first one.

-4(8) - 2y = -20

-32 - 2y = -20

-2y =12

y = -6

 

The answer is (8, -6) or x = 8 and y = -6