Solving systems of linear equations with elimination example 1 | Algebra II | Khan Academy

TL;DR

Learn how to solve systems of equations using elimination.

Transcript

Just in case we need to help with more party planning for the king, let's get ourselves some practice with solving systems of equations with simple elimination. And so here's the exercise right over here. We have x minus 4y is equal to negative 18, and negative x plus 3y is equal to 11. So let's try to work this out. I'll get my little scratch pad ... Read More

Key Insights

• 🆘 Rewriting and familiarizing yourself with a problem can help make solving it easier.
• ❓ Eliminating one variable simplifies the system of equations for further calculations.
• 🦻 Dividing or multiplying equations can make the coefficients of a variable equal, aiding in elimination.
• ✅ Checking the solution by substituting the values back into the original equations is crucial for verification.
• ❓ Solving systems of equations using elimination is a useful skill in mathematical problem-solving.
• ❓ Understanding the concept of opposites and coefficients is important in this method.
• ❓ Systems of equations can have unique solutions, no solution, or infinitely many solutions.

Questions & Answers

Q: What is the purpose of eliminating one variable in a system of equations?

By eliminating one variable, we can simplify the equations and solve for the remaining variable, making it easier to find the solution to the system.

Q: How do you determine which variable to eliminate in a system of equations?

Look for opposites or coefficients that can be made equal by multiplying or dividing one or both equations. In this video, the x terms were eliminated because they had opposite signs.

Q: What does it mean for a system of equations to have a solution?

If the system of equations has a unique solution, it means there is one pair of values for the variables that satisfy both equations simultaneously.

Q: Can you substitute the values of the variables back into the original equations to verify the solution?

Yes, substituting the values of x and y back into the equations allows you to check if they satisfy both equations and confirm that they are indeed the solution.

Summary & Key Takeaways

• The video demonstrates how to solve a system of equations using elimination.

• The goal is to eliminate one variable by adding or subtracting the equations.

• After eliminating one variable, solve for the remaining variable to find the solution to the system of equations.