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What is a system of equations?

Back

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

Front

What does it mean for a system of equations to have a unique solution?

Back

It means there is exactly one set of values for the variables that satisfies all equations in the system.

Tags

CCSS.8.EE.C.8B

Front

What does it mean for a system of equations to have no solution?

Back

It means the equations represent parallel lines that never intersect.

Tags

CCSS.8.EE.C.8A

Front

What does it mean for a system of equations to have infinitely many solutions?

Back

It means the equations represent the same line, or coinciding lines, and every point on the line is a solution.

Tags

CCSS.8.EE.C.8A

Front

How do you solve a system of equations by substitution?

Back

1. Solve one equation for one variable. 2. Substitute that expression into the other equation. 3. Solve for the remaining variable.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

How do you solve a system of equations by elimination?

Back

1. Align the equations. 2. Multiply one or both equations to get opposite coefficients for one variable. 3. Add or subtract the equations to eliminate that variable.

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 consists of lines on a coordinate plane, where the intersection points represent the solutions.

Tags

CCSS.8.EE.C.8A

Front

Back

1

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What does the graph of two intersecting lines represent?

Back

It represents a system of equations with a unique solution.

Tags

CCSS.8.EE.C.8A

Front

What does the graph of two parallel lines represent?

Back

It represents a system of equations with no solution.

Tags

CCSS.8.EE.C.8A