Systems of Linear Equations Review

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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

Front

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

Back

The lines representing the equations 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 representing the equations coincide, meaning they are the same line.

Tags

CCSS.8.EE.C.8A

Front

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

Front

How can you determine the number of solutions in a system of linear equations?

Back

By analyzing the slopes and y-intercepts of the lines represented by the equations.

Tags

CCSS.8.EE.C.8B

Front

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

Back

It is represented by lines on a coordinate plane.

Tags

CCSS.8.EE.C.8A

Front

What is the solution to a system of linear equations?

Back

The point(s) where the lines intersect, representing the values of the variables.

Tags

CCSS.8.EE.C.8B

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How do you write a system of equations from a word problem?

Back

Identify the variables, translate the relationships into equations, and express them as a system.

Tags

CCSS.8.EE.C.8C

Front

What is the substitution method in solving systems of equations?

Back

A method where one equation is solved for one variable, and that expression is substituted into the other equation.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the elimination method in solving systems of equations?

Back

A method where equations are added or subtracted to eliminate one variable, making it easier to solve for the other.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6