# Solving a 3 by 3 System of Equations (the most organized way) | Summary and Q&A

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September 28, 2016
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blackpenredpen
Solving a 3 by 3 System of Equations (the most organized way)

## TL;DR

Learn how to solve a 3+3 system of equations using elimination, choosing the lowest common multiple of the coefficients.

## Key Insights

• 😘 The lowest common multiple of the coefficients is used to determine which variable to eliminate first in a 3+3 system.
• 🥅 The goal of elimination is to create a simplified system with just two variables, which can be further solved using the same elimination method.
• ✖️ The process involves multiplying the equations by the LCM and combining them to cancel out the chosen variable.
• 👻 Substituting the found values back into one of the original equations allows for solving the remaining variable.

## Transcript

okay let's see how to solve this 3+ three system of equations and this is also one of the questions on my test let's see should we eliminate X or Y or Z up to you right if you want to eliminate X you have to First Look for the lowest common multiple of 1 five and three and that will be what 15 and if you want to eliminate y first you have to look f... Read More

### Q: How do you determine which variable to eliminate first in a 3+3 system of equations?

The variable to eliminate first in a 3+3 system is determined by choosing the lowest common multiple of the coefficients of that variable. The goal is to make the coefficients of the chosen variable the same, with alternating signs.

### Q: Can you explain the process of elimination in a 3+3 system of equations?

In a 3+3 system, elimination involves multiplying the equations by the LCM of the coefficients of the chosen variable. This makes the coefficients of the chosen variable the same, with alternating signs. The resulting system can then be combined to eliminate the chosen variable and solve for the remaining variables.

### Q: What should be done if the coefficients of the variables don't share a common multiple in a 3+3 system?

If the coefficients of the variables don't share a common multiple, it is not possible to eliminate a variable. In this case, another method, such as substitution or matrix methods, should be used to solve the system.

### Q: Is it necessary to choose the variable with the lowest coefficients for elimination in a 3+3 system?

No, it is not necessary to choose the variable with the lowest coefficients for elimination in a 3+3 system. The choice of variable for elimination depends on finding the lowest common multiple of the coefficients, which may not always correspond to the variable with the lowest coefficients.

## Summary & Key Takeaways

• To solve a 3+3 system of equations, choose the lowest common multiple (LCM) of the coefficients of one variable as the elimination factor.

• Multiply the equations by the LCM to make the coefficients of the chosen variable the same, with alternating signs.

• Combine the equations to eliminate the chosen variable and solve the resulting 2-variable system using elimination again.

• Substitute the found values into one of the original equations to solve for the remaining variable.

• The final solution for the 3+3 system is obtained by combining the values of all three variables.