Equation 1: ax+by=c equation 2: dx+ey=f which of the following could replace equation 1 and still have the same solution? select all that apply. a. a multiple of the 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 coefficient of x in equation 1 and equation 2. d. the sum of a multiple of equation 1 and equation 2.

A, B, D

If you take selection D to mean any multiple of Equation 1 added to any (possibly different) multiple of Equation 2, then that selection includes the cases described in selections A and B.

As long as the properties of equality are observed, and the operations performed are reversible (can be undone to give the original equations), those operations are allowed.

Appropriate selections are A, B, D.

Comment on this question

These transformations form the basis for methods of solution of systems of linear equations.