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# Systems of equations: FAQ

## What is a system of equations?

A system of equations is a set of two or more equations that all use the same variables. We can try to solve the system by finding values for the variables that make all of the equations true at the same time.

## What are some real-world applications of systems of equations?

Systems of equations can be used to model lots of different situations. For example, if we're trying to figure out how many adult and child tickets were sold at a movie theater, we might set up a system of equations with one equation for the total number of tickets and another equation for the total amount of money collected. We could also use systems of equations to model things like mixtures of solutions, distances and speeds of moving objects, or costs and quantities of different items.

## What's the difference between substitution and elimination?

Both substitution and elimination are methods for solving systems of equations. With substitution, we isolate one of the variables in one of the equations and then substitute that variable into the other equation. With elimination, we add or subtract the two equations in order to eliminate one of the variables.

## Can a system of equations have more than one solution?

Yes! A system of linear equations can have no solutions, one solution, or infinitely many solutions. Sometimes we can tell from looking at the system, and other times we may need to use substitution, elimination, or graphing to figure it out.

## Want to join the conversation?

• Are there any clues or shortcuts to decide to use substitution or elimination? I noticed some equation systems are more easily solved one way than the other.
[My apologies if I missed that somewhere!]
• You can easily eliminate if you notice that the coefficient of a variable has the same magnitude in both equations
• these word problems are bustin me
• no that ok
• what the difference between substitution and elimination
• Substitution and elimination are two different methods that can be used to solve a system of equations.

Substitution: It's easier to use if you already have an equation that is in the form of y = something, or x = something.

Elimination: If the two xs or ys can be subtracted from each other, this method is ideal. It's better if the equations are in standard form.

This is just a basic rundown of the topic. If you still need more help, there are many resources online as well.

I hope this post helped!