Systems of Equations

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What is a system of equations?

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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 for a system of equations to have a unique solution?

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

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CCSS.8.EE.C.8B

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

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It means the equations represent parallel lines that never intersect.

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CCSS.8.EE.C.8A

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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

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How do you solve a system of equations by substitution?

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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

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How do you solve a system of equations by elimination?

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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

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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, 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

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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