Consider the following system: equation 1: ax + by = c equation 2: dx + ey = f a, b, c, d, e, and f are non- zero real numbers. which of the following can replace equation one and still have the same solution? select all that apply.

You did not include the choices. However, I answered one that just included them. I've included the possible answers below and then the correct answers. 

A multiple of Equation 1. 
B. The sum of Equation 1 and Equation 2 
C. An equation that replaces only the coefficient of x with the sum of the coefficients of x in Equation 1 and Equation 2. 
D. An equation that replaces only the coefficient of y with the sum of the coefficients of y in Equation 1 and Equation 2. 
E. The sum of a multiple of Equation 1 and Equation 2.

A, B and E.

Adding and multiplying the terms allow them to keep working. However, you must make sure that each variable is changed each time. Not just one as in C and D.