Question

Use Gauss-Jordan elimination to solve the following linear system:
–3x + 4y = –6
5x – y = 10

A. (2,2)
B. (2,–5)
C. (–6,2)
D. (2,0)

Answer 1

-3x + 4y = -6

20x - 4y = 40
-----------------------
17x = 34

x = 2

5(2) - y = 10

10 - y = 10

y = 0

the correct answer is D. (2,0)

Answer 2

Answer with explanation:

The two equation in two variable are:

  –3 x + 4 y = –6

5 x – y = 10

Writing the equation in terms of Reduced row echelon form and then solving

$\left[\begin{array}{ccc}-3&4&-6\\5&-1&10\end{array}\right]\\\\R_{2}\rightarrow 3R_{2}+5 R_{1}\\\\\left[\begin{array}{ccc}-3&4&-6\\0&17&0\end{array}\right]\\\\R_{1}\rightarrow -4R_{2}+17 R_{1}\\\\ \left[\begin{array}{ccc}-3&0&-6\\0&17&0\end{array}\right]\\\\ -3 x= -6\\\\x=\frac{-6}{-3}\\\\x=2\\\\ 17 y=0\\\\y=0$

Option D: (2,0)