Solve using row reduction ( matrix method)

Question

2x+3y=-8

x-4y=7

Answer 1

The matrix is set up using the coefficients of the variables

 

2X + 3Y = -8

 X - 4Y = 7

 

This yields a matrix of:

 

2   3   -8

1  -4    7

 

The last column is the far side of the equal sign

We want to get a row to look like:  0   1   C    where C is a number

 

We can multiply rows by numbers, we can add rows together... etc...

In essence we solve this just like we did in the elimination method

 

We can make the 2nd row have a 0 in the first position of we multiply it by -2 and then add to the first row

 

2   3   -8

-2  8   -14  (row 2 times '-2')

 

2   3   -8

0  11  -22   (row 1 + row 2)

 

Now we can make this 2nd row look like 0   1   C   if we divide it by 11

 

2   3    -8

0   1    -2   (row 2 divided by 11)

 

Since the numbers represent the coefficients with the last column being the far side of the = sign we now have

0X + Y = -2  or Y = -2

 

We can now use the fact that Y = -2 to substitute back into the 1st row giving

 

2X + 3(-2) = -8

2X - 6 = -8

2X = -2

X = -1

 

Thus we see that X = -1, Y = -2