Systems of Equations Basics Review

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What is a system of equations?

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A system of equations is a set of two or more equations with the same variables. The solution is the point(s) where the equations intersect.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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What does it mean to solve a system of equations graphically?

Back

To solve a system of equations graphically means to plot the equations on a graph and find the point(s) where they intersect.

Tags

CCSS.8.EE.C.8B

Front

What is an ordered pair?

Back

An ordered pair is a pair of numbers used to represent a point in a coordinate system, written as (x, y).

Tags

CCSS.HSA.CED.A.3

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

Back

A system of equations has no solution if the lines represented by the equations are parallel and never intersect.

Tags

CCSS.8.EE.C.8A

Front

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

Back

A system of equations has infinitely many solutions if the equations represent the same line, meaning they intersect at every point on that line.

Tags

CCSS.8.EE.C.8B

Front

How do you determine if an ordered pair is a solution to a system of equations?

Back

To determine if an ordered pair is a solution, substitute the x and y values into each equation. If both equations are true, the pair is a solution.

Front

Back

The solution is (1, 3).

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the graphical representation of a system of equations?

Back

The graphical representation of a system of equations consists of the lines or curves plotted on a coordinate plane that correspond to each equation.

Tags

CCSS.8.EE.C.8B

Front

What does it mean for two equations to be consistent?

Back

Two equations are consistent if they have at least one solution, meaning their graphs intersect at one or more points.

Tags

CCSS.8.EE.C.8B

Front

What does it mean for two equations to be inconsistent?

Back

Two equations are inconsistent if they have no solutions, meaning their graphs do not intersect.

Tags

CCSS.8.EE.C.8A