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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?

• If I was solving a systems of equation and I could use both substitution and elimination, which one is better? Is substitution or elimination better?
• Most of the time, elimination is better as it is faster than substitution, but it is your choice as both are good options for solving a systems of equations question.
• who is ready for quiz 2 and unit test
• I'm not haha.
• how to do this
• If we can think of stuff and picture it in our minds, then can someone who was born blind do the same thing?
• It just takes a lot of time to finally understand this concept
• I can usually understand math equations quickly, but I always trip on the word problems. It adds the extra step of translating phrases into terms, which I am bad at. Any Tips?
• step one: eliminate all info that doesn't matter
step two: replace objects/names with variables (for example, apples would be a, or dollars might be d)
step three: drop words for symbols and rearrange
Hope this makes sense!
(1 vote)
• We are struggling with lesson 5 of this unit. Are there more basic problems we can work with. The problems in this lesson seem very advanced.
• wait a sec what is this again
• Systems of equations.
In a system, you have 2 equations with 2 variables involved, usually `x` and `y`. Solutions to the system are the values of `x` and `y` which satisfy both equations in the system.

Methods to solve:
- Elimination
1) Identify the variable that you can eliminate.
2) Change an equation so that the identified variable's coefficients in both equations match if they don't already.
3) Add/subtract one equation from the other equation to eliminate the variable. Choose + or - wisely, so that they cancel.
4) Solve for the remaining variable, then plug it into any equations to get the eliminated variable.
- Substitution
1) Isolate one of the variables in one of the equations.
2) Plug it into the other equation then solve for the other variable.
3) Use the first equation again to get the value of the first variable.
(1 vote)
• Do you have an example?
(1 vote)
• See the previous sections to this Unit.