given a system of equations, list three ways that we can write new equations that can be used to create equivalent systems

See explanation

Step-by-step explanation:

Given a system of equations, you can

rewrite one of the equations and write the sum of two equations instead of the second equation; rewrite one of the equations and write the difference of two equations instead of the second equation; rewrite one of the equations and write the sum of the first equation multiplied by one nonzero number and the second equation multiplied by another nonzero number instead of the second equation.

These actions are called elementary row operations. Elementary operations with system of equations do not change the solution set.