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

Question

Hello just very lost on how to use the echelon method to solve the system of two equations in two unknowns. Also, what does that mean to have two unknowns?

the question is

x + y = 5

2x -2y = 2

Answer 1

The two unknowns are x and y in this case.

The row echelon method is to put the coefficients into a matrix and reduce to the row echelon form.

[1 1 5]

[2 -2 2]

Row2 = Row2 - 2Row1

[1 1 5]

[0 -4 -8]

Row2 = Row2/-4

[1 1 5]

[0 1 2]

Row1 = Row1- Row2

[1 0 3]

[0 1 2]

Which is in reduced row echelon form (RREF)

x=3

y=2

Verify 3+2=5 and 6-4=2

Answer 2

Use the echelon method to solve each system of two equations in two unknowns; the question is: 

x + y = 5

2x -2y = 2

Detailed Solution:

This is very simple system that can be solved easily by elimination, no need for echelon method

x + y = 5 <== (Equation 1)

2x - 2y = 2 <== (Equation 2)

2(x + y = 5) <== (Equation 1)

2x - 2y = 2 <== (Equation 2)

2x + 2y = 10 <== (Equation 1)

2x - 2y = 2 <== (Equation 2)

Equation 1 + Equation 2 ==> 4x = 12 ==> x = 12/4 ==> x = 3

Substitute x = 3 into Equation 1

x + y = 5 ==> 3 + y = 5 ==> y = 5 – 3 ==> y = 2

(x, y) = (3, 2) <== Final Solution

Use TI-84 Plus to solve:

* Go to: 2nd Matrix ==> Create Matrix A (2 rows x 3 columns) ==> Enter the coefficients/values

* Go to: 2nd Matrix ==> Math ==> rref(A)  ==> (x, y) = (3, 2) <== Result