Systems of equations with elimination (and manipulation) | High School Math | Khan Academy

TL;DR

Learn how to solve systems of equations using elimination by multiplying equations to cancel out variables.

Transcript

Let's solve a few more systems of equations using elimination, but in these it won't be kind of a one-step elimination. We're going to have to massage the equations a little bit in order to prepare them for elimination. So let's say that we have an equation, 5x minus 10y is equal to 15. And we have another equation, 3x minus 2y is equal to 3. And I... Read More

Key Insights

• 🪜 Elimination involves adding or subtracting equations to eliminate variables.
• ❓ Multiplying equations can be used to manipulate them and facilitate the elimination process.
• 😥 The goal is to find the values of the variables that satisfy both equations and represent the point of intersection on a graph.
• 👻 The cancellation of variables simplifies the equations and allows for easier solving of the system.
• ❓ Verifying the solution by substituting it back into one of the original equations ensures its validity.
• ❓ Systems of equations can be solved using elimination, substitution, or graphing methods.
• ✖️ Manipulating equations through multiplication is a common strategy in the elimination process.

Questions & Answers

Q: How can elimination be used to solve systems of equations?

Elimination involves adding or subtracting equations to eliminate variables. This is done by ensuring that the coefficients of the variables in both equations are either the same or the negatives of each other.

Q: Why is multiplying the equations necessary in some cases?

Multiplying the equations allows us to manipulate them in a way that the coefficients of the variables can be made equal or opposite. This is crucial for eliminating the variables and finding their values.

Q: What is the purpose of canceling out variables in the elimination process?

Canceling out variables simplifies the equations and allows us to focus on solving for the remaining variable. It reduces the system of equations to a single equation with one variable.

Q: How can we verify that the solution satisfies both equations?

We can substitute the values of the variables back into one of the original equations and check if the equation holds true. If it does, the solution is valid for both equations.

Summary & Key Takeaways

• Systems of equations can be solved using elimination by adding or subtracting equations to eliminate variables.

• In some cases, the equations may need to be manipulated by multiplying them to cancel out variables.

• The goal is to find the values of the variables that satisfy both equations and represent the point of intersection on a graph.