If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

Main content

Unit: System of equations

Systems of equations overview

Learn
Systems of equations: trolls, tolls (1 of 2)
(Opens a modal)
Systems of equations: trolls, tolls (2 of 2)
(Opens a modal)
Systems of equations with elimination: King's cupcakes
(Opens a modal)
Systems of equations with elimination: potato chips
(Opens a modal)
Systems of equations with substitution: potato chips
(Opens a modal)
Systems of equations number of solutions: fruit prices (1 of 2)
(Opens a modal)
Systems of equations number of solutions: fruit prices (2 of 2)
(Opens a modal)

Introduction to systems of equations

Learn
Systems of equations: trolls, tolls (1 of 2)
(Opens a modal)
Testing a solution to a system of equations
(Opens a modal)
Systems of equations: trolls, tolls (2 of 2)
(Opens a modal)
Systems of equations with graphing: y=7/5x-5 & y=3/5x-1
(Opens a modal)
Systems of equations with graphing: exact & approximate solutions
(Opens a modal)
Practice
Solutions of systems of equations
4 questions
Systems of equations with graphing
4 questions

Equivalent systems of equations and the elimination method

Learn
Systems of equations with elimination: King's cupcakes
(Opens a modal)
Systems of equations with elimination: x-4y=-18 & -x+3y=11
(Opens a modal)
Systems of equations with elimination: potato chips
(Opens a modal)
Systems of equations with elimination (and manipulation)
(Opens a modal)
Why can we subtract one equation from the other in a system of equations?
(Opens a modal)
Worked example: equivalent systems of equations
(Opens a modal)
Worked example: non-equivalent systems of equations
(Opens a modal)
Solving systems of equations by elimination (old)
(Opens a modal)
Elimination method review (systems of linear equations)
(Opens a modal)
Equivalent systems of equations review
(Opens a modal)
Practice
Systems of equations with elimination
4 questions
Systems of equations with elimination challenge
4 questions
Reasoning with systems of equations
4 questions

Solving systems of equations with substitution

Learn
Systems of equations with substitution: potato chips
(Opens a modal)
Systems of equations with substitution: -3x-4y=-2 & y=2x-5
(Opens a modal)
Solving linear systems by substitution (old)
(Opens a modal)
Substitution method review (systems of equations)
(Opens a modal)
Practice
Systems of equations with substitution
4 questions

Manipulating expressions with unknown variables

Learn
Manipulating expressions using structure
(Opens a modal)
Manipulating expressions using structure (example 2)
(Opens a modal)
Practice
Manipulate expressions using structure
4 questions

Number of solutions to systems of equations

Learn
Systems of equations number of solutions: fruit prices (1 of 2)
(Opens a modal)
Systems of equations number of solutions: fruit prices (2 of 2)
(Opens a modal)
Solutions to systems of equations: consistent vs. inconsistent
(Opens a modal)
Solutions to systems of equations: dependent vs. independent
(Opens a modal)
Number of solutions to a system of equations
(Opens a modal)
Number of solutions to a system of equations graphically
(Opens a modal)
Number of solutions to a system of equations algebraically
(Opens a modal)
How many solutions does a system of linear equations have if there are at least two?
(Opens a modal)
Number of solutions to system of equations review
(Opens a modal)
Practice
Number of solutions to a system of equations graphically
4 questions
Number of solutions to a system of equations algebraically
4 questions

Systems of equations word problems

Learn
Age word problem: Imran
(Opens a modal)
Age word problem: Ben & William
(Opens a modal)
Age word problem: Arman & Diya
(Opens a modal)
System of equations word problem: walk & ride
(Opens a modal)
System of equations word problem: no solution
(Opens a modal)
System of equations word problem: infinite solutions
(Opens a modal)
Systems of equations with elimination: TV & DVD
(Opens a modal)
Systems of equations with elimination: apples and oranges
(Opens a modal)
Systems of equations with substitution: coins
(Opens a modal)
Systems of equations with elimination: coffee and croissants
(Opens a modal)
Practice
Age word problems
4 questions
Systems of equations word problems
4 questions
Systems of equations word problems capstone
4 questions

Solving equations by graphing (Algebra 2 level)

Learn
Interpreting equations graphically
(Opens a modal)
Interpreting equations graphically (example 2)
(Opens a modal)
Solving equations graphically (1 of 2)
(Opens a modal)
Solving equations graphically (2 of 2)
(Opens a modal)
Solving equations graphically
(Opens a modal)
Practice
Interpret equations graphically
4 questions
Solve equations graphically
4 questions

Systems with three variables

Learn
Intro to linear systems with 3 variables
(Opens a modal)
Solving linear systems with 3 variables
(Opens a modal)
Solving linear systems with 3 variables: no solution
(Opens a modal)
3-variable linear system word problem
(Opens a modal)

Unit test

Test your understanding of System of equations with these 14 questions.

About this unit

This topic covers: - Solutions of linear systems - Graphing linear systems - Solving linear systems algebraically - Analyzing the number of solutions to systems - Linear systems word problems