Systems of Linear Equations

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What is a system of linear equations?

Back

A set of two or more linear equations with the same variables.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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What does it mean if a system of linear equations has no solution?

Back

The lines representing the equations are parallel and never intersect.

Tags

CCSS.8.EE.C.8A

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What does it mean if a system of linear equations has one solution?

Back

The lines intersect at exactly one point.

Tags

CCSS.8.EE.C.8A

Front

What does it mean if a system of linear equations has infinitely many solutions?

Back

The lines coincide, meaning they are the same line.

Tags

CCSS.8.EE.C.8A

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What are the three main methods to solve systems of equations?

Back

Graphing, Substitution, Elimination.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

How do you determine if a point is a solution to a system of equations?

Back

Substitute the point into both equations; if it satisfies both, it is a solution.

Front

What is the elimination method?

Back

A method for solving systems of equations by adding or subtracting equations to eliminate a variable.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the substitution method?

Back

A method for solving systems of equations by solving one equation for a variable and substituting that expression into the other equation.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

Solve the system: 2x + 3y = 6 and x - y = 1. What is the solution?

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(3, 0) is the solution.

Tags

CCSS.HSA.REI.C.9

Front

What is the graphical representation of a system of linear equations?

Back

The lines representing the equations on a coordinate plane.

Tags

CCSS.8.EE.C.8A