Use the echelon method to solve the given system of two equations in two unknowns

Question

x/5+y=1/5

x/7+y=-3/7

Answer 1

Hi Emily, the first thing I would do is multiply the first row by 5 and the second row by 7 to clear the fractions.

 

The equations become:

 

x  + 5y  =   1

x  + 7y  = -3

 

Set up the matrix:

 

1   5    1

1   7  -3

 

Multiply the first row by -1 and add to the second row:

 

1   5   1

0   2  -4

 

Divide the second row by two:

 

1   5   1

0   1  -2

 

Multiply the second row by -5 and add to the first row:

 

1   0   11

0   1   -2

 

The answer to the system is:

 

x = 11 and y = -2

 

Check:

 

Original first equation:

 

11/5 - 2 = 1/5

 

11/5 - 10/5 = 1/5

 

1/5 = 1/5

 

Original second equation:

 

11/7 - 2 = -3/7

 

11/7 - 14/7 = -3/7

 

-3/7 = -3/7

 

Questions?