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 eliminates the need for further calculation
c. it reduces the system to a single variable
d. it simplifies the graphing process

1. what is the first step in the substitution method when solving systems of linear equations?

a. multiply the equations
b. solve one equation for one variable
c. add the equations together
d. plot the equations on a graph

Explanation:

1. Substitution works by replacing one variable with an expression from the other equation, which isolates a single variable, simplifying the system to solve step-by-step. Options b, c, and d are incorrect: further calculation is still needed, it does not always reduce to a single variable (only one variable is isolated at a time), and it does not relate to graphing simplification.
2. The substitution method requires first rearranging one equation to express one variable in terms of the other, which is the foundational first step before substituting into the second equation. The other options describe steps for other methods (elimination, graphing) or are not the starting action for substitution.

Answer:

1. a. It isolates one variable, making the system easier to solve
2. b. Solve one equation for one variable