Intro to Systems of Equations

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What is a system of equations?

Back

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

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What does it mean if two lines intersect in a system of equations?

Back

It means there is one unique solution to the system.

Tags

CCSS.8.EE.C.8A

Front

What are parallel lines in the context of systems of equations?

Back

Parallel lines have no solutions because they never intersect.

Tags

CCSS.8.EE.C.8A

Front

What does it mean if two equations represent the same line?

Back

It means there are infinitely many solutions to the system.

Tags

CCSS.8.EE.C.8B

Front

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

Back

Substitute the point's coordinates into each equation; if both equations are true, it's a solution.

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What is the graphical representation of a system of equations?

Back

The graphical representation consists of lines on a coordinate plane.

Tags

CCSS.8.EE.C.8B

Front

What is the solution to the system of equations y = 2x + 1 and y = 3x - 2?

Back

(3, 7)

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the substitution method in solving systems of equations?

Back

A method where one equation is solved for one variable, and then 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.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

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

Back

It means the lines are parallel and do not intersect.

Tags

CCSS.8.EE.C.8A