Can anyone help me with this question? I would really appreciate it!

Question

1. Solve the system of linear equations, using the Gauss-Jordan elimination method. (If there is no solution, enter NO SOLUTION. If there are infinitely many solutions, express your answer in terms of the parameters t and/or s.)

2x	−	y	=	3
x	+	2y	=	14
2x	+	3y	=	23

(x, y) = ( )

Answer 1

Solve the system of linear equations, using the Gauss-Jordan elimination method. (If there is no solution, enter NO SOLUTION. If there are infinitely many solutions, express your answer in terms of the parameters t and/or s.)

2x − y = 3  ==> (1)

x + 2y = 14 ==> (2)

2x + 3y = 23 ==> (3)

Detailed Solution:

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eqn (3) - eqn (1) ==> (2x + 3y = 23) - (2x − y = 3) ==> (4y = 20) ==> y = 5

Substitute y = 5 into any eqn (1) or (2) or (3). Ok, Substitute y = 5 into eqn (2)

x + 2y = 14 ==> x + 2(5) = 14 ==> x = 14 - 10 ==> x = 4

Final Solution: (x, y) = (4, 5)

Check The Solution: (x, y) = (4, 5)

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2x − y = 3  ==> (1): 2(4) − 5 = 3 ==> 8 − 5 = 3 ==> 3 = 3

x + 2y = 14 ==> (2): 4 + 2(5) = 14 ==> 4 + 10 = 14 ==> 14 = 14

2x + 3y = 23 ==> (3): 2(4) + 3(5) = 23 ==> 8 + 15 = 23 ==> 23 = 23

Note: As you can see above, this system of linear equations is easily solved using elimination method (No need for Gauss-Jordan elimination method). You can also create Matrix A (3X3) in TI-84 Plus and using rref(A) to solve/verify.