(Q17) Sample #1, Math 141/146 common final, Solve system of equations by substitution  Summary and Q&A
TL;DR
Use the substitution method to isolate a variable in an equation, substitute it into the other equation, and solve for the remaining variable.
Questions & Answers
Q: What is the first step in solving equations using the substitution method?
The first step is to choose a variable to isolate, preferably one with a coefficient of 1 or no coefficient at all.
Q: How does substituting one equation into another help in solving the system of equations?
Substituting one equation into another allows us to eliminate one variable and solve the remaining equation for the other variable.
Q: Can any variable be chosen for isolation in the substitution method?
Yes, any variable can be chosen for isolation as long as it simplifies the equations and makes the substitution process easier.
Q: What should be done when substituting the isolated variable into the other equation?
The isolated variable should be substituted into the equation that was not used for isolation. Plugging it into the original equation can lead to errors.
Q: How do we combine terms and simplify the equation after substituting the isolated variable?
We distribute any coefficients, combine like terms, and perform necessary operations to simplify the equation before solving for the variable.
Q: Is it necessary to check the solution obtained from the substitution method?
Yes, it is always recommended to check the solution by substituting the values back into the original equations to ensure they satisfy both equations.
Summary & Key Takeaways

The content explains how to solve equations using the substitution method.

It shows the stepbystep process of isolating a variable and substituting it into the other equation.

It provides an example of solving a system of equations using substitution.