# System of Equations with Three Equations and Three Variables | Summary and Q&A

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November 29, 2014
by
The Math Sorcerer
System of Equations with Three Equations and Three Variables

## TL;DR

Learn how to solve a system of equations by eliminating variables using basic arithmetic operations.

## Key Insights

• ❓ Elimination is a common method for solving systems of equations.
• ❓ The choice of equations for elimination is significant to simplify the problem.
• ❓ Back substitution is useful for finding the values of the eliminated variables.

## Transcript

solve the given system of equations so let's go ahead and work this out now there's lots of ways to do this we're going to take a really basic approach so i'm going to number these one two and three so we've numbered them and the idea is as follows we're going to pick two equations and get rid of a variable and then we're going to pick another two ... Read More

### Q: What is the basic approach to solving a system of equations through elimination?

The basic approach involves choosing two equations, eliminating a variable by multiplying one or both equations, and then combining the equations to eliminate the targeted variable.

### Q: How do you eliminate a variable from two equations?

To eliminate a variable, multiply one equation by a suitable factor such that when added to the other equation, the targeted variable cancels out.

### Q: What is back substitution?

Back substitution is a technique used to find the values of eliminated variables. After obtaining values for the remaining variables, they can be substituted back into a previous equation to find the value of the eliminated variable.

### Q: Why is it important to be careful when solving systems of equations?

Carelessness can lead to mistakes in arithmetic operations or misinterpretation of the equations, resulting in incorrect solutions. It is crucial to double-check calculations to avoid errors.

## Summary & Key Takeaways

• To solve a system of equations, choose two equations, eliminate a variable, and repeat the process with another pair of equations.

• Multiply the first equation by a suitable factor to eliminate the variable, then combine the equations to solve for the remaining variables.

• Use back substitution to find the values of the eliminated variables, and plug them back into one of the original equations to determine the final solution.