Question

1. how does substituting one equation into another help in solving a system of equations?

a. it isolates one variable, making the system easier to solve
b. it reduces the system to a single variable
c. it simplifies the graphing process
d. it eliminates the need for further calculation

Explanation:

Substitution method for systems of equations works by rearranging one equation to express one variable in terms of the other(s), then substituting this expression into the other equation(s). This isolates a variable, reducing the system to one with fewer variables, which simplifies solving for the unknowns. Option b is incorrect because it reduces to one fewer variable, not necessarily a single variable (for systems with more than two variables). Option c is irrelevant as substitution is an algebraic, not graphical, method. Option d is wrong because further calculation is still needed to find the remaining variables.

Answer:

a. It isolates one variable, making the system easier to solve