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### Course: Algebra 1 > Unit 6

Lesson 6: Systems of equations word problems- Age word problem: Imran
- Age word problem: Ben & William
- Age word problem: Arman & Diya
- Age word problems
- System of equations word problem: walk & ride
- Systems of equations word problems
- System of equations word problem: no solution
- System of equations word problem: infinite solutions
- Systems of equations word problems (with zero and infinite solutions)
- Systems of equations with elimination: TV & DVD
- Systems of equations with elimination: apples and oranges
- Systems of equations with substitution: coins
- Systems of equations with elimination: coffee and croissants
- Systems of equations: FAQ

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# Systems of equations: FAQ

Frequently asked questions about systems of equations

## 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.

Practice with our Solutions of systems of equations exercise.

## 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.

Practice with our Creating systems in context
exercise.

## 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.

Practice with our Systems of equations with substitution exercise.

Practice with our Systems of equations with elimination exercise.

## 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.

Practice with our Number of solutions to a system of equations graphically exercise.

Practice with our Number of solutions to a system of equations algebraically exercise.

## 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!](16 votes)- You can easily eliminate if you notice that the coefficient of a variable has the same magnitude in both equations(12 votes)

- these word problems are bustin me(14 votes)
- what the difference between substitution and elimination(4 votes)
- 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!(10 votes)

- Why are word problems so confusing.(7 votes)
- I was going to wait until the review to write notes ;-;(5 votes)
- if 5+5=55 why does 2+2=22(0 votes)
- The problem with what you are asking is that neither one of those equations are right.(4 votes)

- frick these math quetsions(1 vote)
- Can someone explain how to analyze word problems or drop a link to a video that explains it, please? I've been trying to follow along with these videos but with different problems, and I keep getting them wrong.(1 vote)