Write an augmented matrix for the system. Use row operations to put it in row ecjelon form. Find y then back substitute to find x.

Question

x+3y=-18

3x-y=16

I have the matrix but i'm lost on the rest of it. Please show work.

 

1  3  -18

3 -1   16

Answer 1

That is the correct matrix. The next step is to eliminate from the first entry of the second row. This is done by adding -3 times the first row to the second row. The resulting matrix is:

 

1                3                   -18

3 +(-3)*1   -1+(-3)*3       16+(-3)*(-18)  

 

(Notice that I have multiplied each entry in the first row by -3 and added the result to the corresponding entry in the second row.) 

This simplifies to

 

1      3      -18

3-3   -1-9  16+54,

 

or

 

1  3     -18

0  -10  70

 

Now, we need to get a 1 in the second element of the second row. This is done by dividing the second row by -10:

 

1    3     -18

0    1     -7

 

Depending on your class's definition of row echelon form, either this step or the previous step is row echelon form. 

Assuming it was row echelon form at the previous step, the y equation that you now have is

 

-10y=70,

 

which you can divide by -10 to get

 

y=-7

 

To back substitute in order to find x, you substitute this value into the first equation and solve for x:

 

x+3y=-18

x+3(-7)=-18

x-21=-18

x=3