Linear algebra elementary row operation

Question

State in words the next elementary row operation that should be performed on the system in order to solve it. [More than one answer is possible]

$x_1 + 4x_2 -2x_3 + 8x_4 = 12$

$x_2-7x_3+2x_4=-4$

$5x_3-x_4=7$

$x_3+3x_4=-5$

The answer said the best method would be to interchange the 3rd and 4th equation.I'm confused on why the best would not be to jump right into it, and multiply the 4th equation by -5 and adding it to the 3rd equation, with the result as the new 4th equation.

Answer 1

If you interchange the rows and then perform the operation you mentioned - the matrix will be in upper triangular form. I guess that's what the book is referring to.