Question

question 42 points 1 why does adding a multiple of one equation to another not change the solution of the system? because it multiplies the solution by a constant because it creates a new system with different solutions because it eliminates one variable automatically because it changes only the coefficients but not the solution

Explanation:

When you add a multiple of one equation to another in a system of equations, you are performing an elementary row operation that preserves the solution set. This operation modifies the coefficients of the equations but does not alter the values that satisfy all equations in the system. The other options are incorrect: this operation does not multiply solutions by a constant, does not create a system with different solutions, and does not automatically eliminate a variable (variable elimination requires specific multiples chosen for that purpose).

Answer:

Because it changes only the coefficients but not the solution