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

2x+10y=-12

-3x+y=34
I have the matrix and what to multiply it by except the last one. I'm really lost. Please help and show work. 

2   10     -12     *1/2
-3   1      34

 

1    5     -6    *3

-3   1     34

 

1   5      -6    

0   16     16 

Answer 1

You're actually done with the first part of the problem -- the matrix is in row echelon form and you have done it correctly. The next step is to recognize that this matrix corresponds to the system

 

x+5y=-6

   16y=16

 

To find y, use the second equation:

 

16y=16

y=1

 

Back substituting means substituting this value for y into the first equation and solving for x:

 

x+5(1)=-6

x=-11

 

So the solution is x=-11,y=1. I hope this helps.