Algebra 37 - Solving Systems of Equations by Elimination

TL;DR

The elimination method involves adding equations to eliminate one variable and solve a system of equations.

Transcript

Hello. I'm Professor Von Schmohawk and welcome to Why U. In the last lecture we saw how systems of two linear equations in two variables could be solved to find one solution which simultaneously satisfies both equations. We know that the set of solutions for each equation is visually represented by its graph and each equation's graph is made up of ... Read More

Key Insights

• 🪜 The elimination method involves adding or subtracting equations to eliminate one variable and find solutions to systems of linear equations.
• 💦 The elimination method works best when one of the terms can be cancelled out by choosing appropriate multipliers.
• ✖️ Sometimes, it may be necessary to multiply both equations by different multipliers to eliminate a variable in the elimination method.
• 😫 Adding equations creates a new equation that has a different solution set from the original equations.

Questions & Answers

Q: What is the elimination method used for in solving systems of equations?

The elimination method is used to find solutions to systems of linear equations by adding or subtracting equations to eliminate one variable.

Q: How is the elimination method different from the substitution method?

While the substitution method substitutes one variable in terms of the other, the elimination method involves adding or subtracting equations to eliminate one variable.

Q: How do you choose which variable to eliminate in the elimination method?

In the elimination method, you can choose to eliminate either the x or y variable by adding or subtracting equations with appropriate multipliers.

Q: What happens when the x or y terms cannot be cancelled out in the elimination method?

If the x or y terms cannot be cancelled out, you can multiply both equations by different multipliers, resulting in a new equation where the x or y terms will cancel out.

Summary & Key Takeaways

• The elimination method is used to solve systems of linear equations in standard form.

• By adding or subtracting equations, one variable is eliminated, allowing for the solution of the remaining variable.

• The elimination method can be used when terms can be cancelled out by choosing appropriate multipliers.