Solving Systems of Equations

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What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution to the system is the set of values that satisfy all equations simultaneously.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What are the methods to solve a system of equations?

Back

The main methods to solve a system of equations are: 1) Graphing, 2) Substitution, 3) Elimination.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

How do you use the substitution method to solve a system of equations?

Back

To use the substitution method, solve one equation for one variable, then substitute that expression into the other equation to find the values of the variables.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the elimination method in solving systems of equations?

Back

The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the remaining variable.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What does it mean for a system of equations to be consistent?

Back

A consistent system of equations has at least one solution, meaning the equations intersect at one or more points.

Tags

CCSS.8.EE.C.8B

Front

What does it mean for a system of equations to be inconsistent?

Back

An inconsistent system of equations has no solutions, meaning the equations represent parallel lines that never intersect.

Tags

CCSS.8.EE.C.8B

Front

What is a dependent system of equations?

Back

A dependent system of equations has infinitely many solutions, meaning the equations represent the same line.

Tags

CCSS.8.EE.C.8B

Front

How do you graph a system of equations?

Back

To graph a system of equations, plot each equation on the same coordinate plane and identify the point(s) where the lines intersect.

Tags

CCSS.8.EE.C.8B

Front

What is the first step in solving a system of equations using substitution?

Back

The first step is to solve one of the equations for one variable in terms of the other variable.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the first step in solving a system of equations using elimination?

Back

The first step is to align the equations and manipulate them (if necessary) so that adding or subtracting them will eliminate one variable.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6