using an augmented matix i have to solve the system, but i don't know how?

Question

how do i have the system:
x+2y=3
4x+2y=-6

Answer 1

An augmented matrix is a square matrix formed by the coefficients of the variables with an extra column at the end consisting of the answers. So here (without the matrix brackets) your augmented matrix is

1 2 3
4 2 -6

You need to get the first 2 columns to read
1 0
0 1
So multiply the top row by -4 and add it to the second row getting a new second row:

1..2... 3
0 -6 -18

Divide the second row by -6 to get
1 2 3
0 1 3

Multiply the second row by -2 and add to the first row getting a new first row:

1 0 -3
0 1 3

So x = -3 and y = 3

Be sure to check these in the original equations since I can't type all that well

Answer 2

Your system should be a matrix that looks like this:

|1 2 3 |
|4 2 -6 |

The numbers in the first columns are just the coefficients of x and y in the two equations The numbers in the third columns numerical values of each equation.

To solve, you want to have zeroes everywhere in the first two columns except on the diagonal. In other you wish to get rid of the 2 in the first row and the 4 in the second row, replacing each by zero. You also want all other numbers in columns 1 and 2 to be +1.
So subtract row 1 from row 2 and use result to replace row 1

The matrix now becomes:

|3 0 -9|
|4 2 -6|

Now multiply row 1 by 4 and row 2 by 3 getting:

|12 0 -36|
|12 6 -18|
Now subtract Row 2 from row 1 and use result to replace row 2

|12 0 -36|
|0 -6 -18|

Now divide first row by 12 and second row by -6 giving:

|1 0 -3|
|0 1 3|
We have accomplished what we set out to do. Notice that the third column now contains the solution to the system , namely,
x = -3 and y = 3.